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Maximal ideal

In mathematics, more in ring theory, a maximal ideal is an ideal, maximal amongst all proper ideals. In other words, I is a maximal ideal of a ring R if there are no other ideals contained between I and R. Maximal ideals are important because the quotients of rings by maximal ideals are simple rings, in the special case of unital commutative rings they are fields. In noncommutative ring theory, a maximal right ideal is defined analogously as being a maximal element in the poset of proper right ideals, a maximal left ideal is defined to be a maximal element of the poset of proper left ideals. Since a one sided maximal ideal A is not two-sided, the quotient R/A is not a ring, but it is a simple module over R. If R has a unique maximal right ideal R is known as a local ring, the maximal right ideal is the unique maximal left and unique maximal two-sided ideal of the ring, is in fact the Jacobson radical J, it is possible for a ring to have a unique maximal two-sided ideal and yet lack unique maximal one sided ideals: for example, in the ring of 2 by 2 square matrices over a field, the zero ideal is a maximal two-sided ideal, but there are many maximal right ideals.

There are other equivalent ways of expressing the definition of maximal one-sided and maximal two-sided ideals. Given a ring R and a proper ideal I of R, I is a maximal ideal of R if any of the following equivalent conditions hold: There exists no other proper ideal J of R so that I ⊊ J. For any ideal J with I ⊆ J, either J = I or J = R; the quotient ring. There is an analogous list for one-sided ideals, for which only the right-hand versions will be given. For a right ideal A of a ring R, the following conditions are equivalent to A being a maximal right ideal of R: There exists no other proper right ideal B of R so that A ⊊ B. For any right ideal B with A ⊆ B, either B = A or B = R; the quotient module. Maximal right/left/two-sided ideals are the dual notion to that of minimal ideals. If F is a field the only maximal ideal is. In the ring Z of integers, the maximal ideals are the principal ideals generated by a prime number; the ideal is a maximal ideal in ring Z. Generally, the maximal ideal of Z are of the form where p is a prime number and f is a polynomial in Z, irreducible modulo p.

Every prime ideal is a maximal ideal in a Boolean ring, i.e. a ring consisting of only idempotent elements. In fact, every prime ideal is maximal in a commutative ring R whenever there exists an integer n > 1 such that x n = x for any x ∈ R. More all nonzero prime ideals are maximal in a principal ideal domain; the maximal ideals of the polynomial ring C are principal ideals generated by x − c for some c ∈ C. More the maximal ideals of the polynomial ring K over an algebraically closed field K are the ideals of the form; this result is known as the weak Nullstellensatz. An important ideal of the ring called the Jacobson radical can be defined using maximal right ideals. If R is a unital commutative ring with an ideal m k = R/m is a field if and only if m is a maximal ideal. In that case, R/m is known as the residue field; this fact can fail in non-unital rings. For example, 4 Z is a maximal ideal in 2 Z. If L is a maximal left ideal R/L is a simple left R-module. Conversely in rings with unity, any simple left R-module arises this way.

Incidentally this shows that a collection of representatives of simple left R-modules is a set since it can be put into correspondence with part of the set of maximal left ideals of R. Krull's theorem: Every nonzero unital ring has a maximal ideal; the result is true if "ideal" is replaced with "right ideal" or "left ideal". More it is true that every nonzero finitely generated module has a maximal submodule. Suppose I is an ideal, not R. R/I is a ring with unity, so the above theorems can be applied to the quotient to conclude that there is a maximal ideal of R containing I. Krull's theorem can fail for rings without unity. A radical ring, i.e. a ring in which the Jacobson radical is the entire ring, has no simple modules and hence has no maximal right or left ideals. See regular ideals for possible ways to circumvent this problem. In a commutative ring with unity, every maximal ideal is a prime ideal; the converse is

2015 Malmö FF season

The 2015 season was Malmö FF's 104th in existence, their 80th season in Allsvenskan and their 15th consecutive season in the league. They competed in Allsvenskan where they finished fifth, 2014–15 Svenska Cupen where they were knocked out in the quarter-finals and the 2015–16 UEFA Champions League where they were knocked out in the group stage. Malmö FF participated in one competition in which the club continued playing in for the 2016 season, 2015–16 Svenska Cupen; the season began with the group stage of Svenska Cupen on 22 February, league play started on 6 April and concluded on 31 October. The season concluded with the last Champions League group stage match on 8 December. Markus Rosenberg was appointed permanent club captain, succeeding Guillermo Molins, who he had temporarily replaced during the summer of 2014 due to Molins being injured. For the first time in the history of the club, Malmö FF appeared in consecutive UEFA Champions League group stages; the club was not as successful on the domestic stage as they failed to defend their title by finishing fifth in the league.

This was the first time. The league season started on 6 April 2015 and concluded on 31 October 2015; the official season fixtures were released on 21 January 2015. Malmö FF started the season away against newly promoted GIF Sundsvall on 6 April, Malmö FF won the match 4–1; the club's first home fixture was played on 9 April against last year's third-place team AIK, the match ended in a goalless draw. There was a one-month summer break in June due to Sweden's participation in the 2015 UEFA European Under-21 Championship in the Czech Republic. Malmö FF played no league matches 5 July; the club played its last league fixture of the season at home against IFK Norrköping on 31 October, a 2–0 defeat which saw Norrköping become league champions. The club got off to a promising start, winning three of the first five games against GIF Sundsvall, title contenders and rivals IFK Göteborg and newly promoted Hammarby IF. Out of these first five games Malmö FF tied against title rivals AIK and Falkenbergs FF.

Notably Malmö FF dropped pole position in the league to Gefle IF on 9 April in the second round of play. The club had held first place in the league since 18 August 2013 for a continuous streak of 599 days, never losing the lead during the victorious 2014 season. Malmö FF continued to win the following two games at home against Halmstads BK and regional rivals Helsingborgs IF; these two wins solidified the club's position as league leaders after seven rounds of play. The following three matches resulted in a win-less streak of two losses in a row. Malmö FF first tied the away fixture against IF Elfsborg after a late equaliser from the home side; this was succeeded by defeats against BK Häcken and Kalmar FF, notably the last time Malmö FF won against Häcken was as far back as in October 2011. This was the first time since September 2014 that the club failed to win in three games and the first time since June 2011 that they lost two league matches in succession; this streak was followed by back to back wins against Åtvidabergs FF and Gefle IF and a home draw against Djurgårdens IF.

This meant that Malmö FF took up fourth position in the league table at the time of the summer break, seven points behind leaders IFK Göteborg. When Allsvenskan restarted in July, Malmö FF experienced another struggling period as they failed to win any of the first three matches after the break, an away loss against IFK Norrköping and two consecutive draws against Örebro SK; this was followed by a four-match undefeated streak in which Malmö FF defeated GIF Sundsvall, league leaders IFK Göteborg and drew against Åtvidaberg. After 20 rounds of play, Malmö FF was in fifth place in the league, four points behind IFK Göteborg in first place. In the next-coming five games, the club drew one and lost one. By 25 rounds the gap to the trio of leading teams had increased to seven points and Malmö FF was now forth, one point ahead of Elfsborg. With five matches remaining, Malmö FF still had a realistic chance of retaining the title if they won the remaining fixtures; that chance vanished with a goalless draw away at Halmstad and an away loss against fellow title contender AIK in the 27th round.

The primary focus for Malmö FF now was to reach a fourth-place finish. After wins against Kalmar and Hammarby in the 28th and 29th round Malmö FF had a two-point advantage over Elfsborg for fourth place. In the last round, Malmö FF played a home fixture against league leaders IFK Norrköping. A draw would have sufficed for Malmö FF to clinch fourth place, but a motivated Norrköping won the match 2–0 and captured their first league title in 26 years. Since Elfsborg won their last match, Malmö FF ended the season in fifth place. Malmö FF qualified for the group stage of the 2014–15 Svenska Cupen in the 2014 season by beating IS Halmia 2–1 on 15 November 2014; the club were seeded first in the group stage draw after finishing first in the 2014 Allsvenskan. The groups were drawn on 19 November 2014. Malmö FF drew Jönköpings Södra IF who finished fourth in Superettan for the 2014 season, Assyriska FF who finished 14th in the same league and Hudiksvalls FF who finished second in Division 2 Norrland; the group stage was played between 22 February and 7 March 2015 before the start of the league season.

Malmö FF beat Assyriska 3–0 in the opening group fixture at Malmö IP on 22 February 2015. In the second round, the club travelled to Hudiksvall and won 5–0 on 28 February 2015. In the last group match Malmö FF faced Jönköpings Södra at Malmö IP and won 4–0 on 7 March 2015; these results positioned Malmö FF top of the group table and the club advanced to the quarter-finals. The quarter finals were drawn on 9 March 2015, Malmö FF

Kings XI Punjab in 2018

The 2018 season is the 11th season for the Indian Premier League franchise Kings XI Punjab. Steve Smith is captaining the team for the season. In December 2017, Brad Hodge was appointed head coach of the team In March 2018, Venkatesh Prasad, Nishanta Bordoloi and Shyamal Vallabhjee were appointed bowling coach, fielding coach and technical coach In December 2017, the franchise requested the BCCI to shift its home from Mohali, Chandigarh, to some other city; the BCCI, rejected the plea after some members of the IPL Governing Council opposed the idea. According to The Times of India, two BCCI officials pointed out that charging the franchise a few extra crores for shifting the base would not be a reasonable idea since the valuation for the home shift would be difficult to calculate. On 13 March 2018, Kings XI Punjab unveiled their official jersey for the season while Kent RO Systems was announced as the chief sponsor of the team in a joint press conference. On 16 March 2018, the Punjab Cricket Association requested the BCCI to reschedule some of Kings XI Punjab's home matches as Chandigarh Airport was to remain shut from 12 May to 31 May due to maintenance work.

The team was supposed to play four home matches at the Punjab Cricket Association IS Bindra Stadium in Mohali from 4 May to 14 May, whereas the earlier home matches in April were scheduled to be held at Indore. On 20 March 2018, the franchise revealed their revised schedule, with Mohali hosting the first three home matches and Indore hosting the remaining four. Players with international caps are listed in bold. * denotes a player, unavailable for selection. * denotes a player, unavailable for rest of the season. Owners - Ness Wadia, Preity Zinta, Mohit Burman, Karan Paul Chief Executive Officer - Satish Menon Chief Operating Officer - Rajeev Khanna Team manager - Major Varoon Parmar Head of cricket operations and strategy - Virender Sehwag Head coach - Brad Hodge Assistant coach - Mithun Manhas Bowling coach - Venkatesh Prasad Fielding coach - Nishanta Bordoloi Strength & conditioning coach - Nishant Thakur Technical coach - Shayamal Vallabhjee Video analyst - Ashish Tuli Physiotherapist – Amit Tyagi The four top ranked teams qualify for the playoffs advanced to Qualifier 1 advanced to the Eliminator All times are in Indian Standard Time Last Update: 31 March 2018.

Source: Cricinfo Last Update: 31 January 2018. Source: Cricinfo

Kurt Ahrens Jr.

Kurt Karl-Heinrich Ahrens known as Kurt Ahrens Jr. is a former sports car racing and touring car racing driver who appeared in German Grand Prix races in Formula 2 cars. His father, Kurt Ahrens Sr. was a German speedway champion who competed against his son for five years. Kurt Ahrens Jr. started in 1958 with a Cooper-Norton Formula 3 and won the German Formula Junior title in 1961 and 1963, when his father retired. He raced Formula 2 and was present when Jim Clark was killed at the Hockenheimring in 1968. Due to the long Nürburgring track, it was possible to take part in the German Grand Prix in Formula 2 cars, he participated with Brabhams for the Caltex Racing team, was invited to drive the Brabham-Repco F1 in the wet 1968 German Grand Prix. In 1968, Ahrens Jr. joined the Porsche factory sports car team and shared victory with Jo Siffert in the 1969 Austrian 1000 km event. He co-drove the pole-setting Porsche 917 "long tail" at the 1969 24 Hours of Le Mans and the 1970 24 Hours of Le Mans, but neither car finished.

In 1970, he partnered with Vic Elford to win the 1000km Nürburgring in a Porsche 908. Ahrens retired after 1970, he had suffered a high speed shunt in April 1970 while testing a long tail Porsche on a wet Ehra-Lessien, with the car disintegrating badly- the car went under the Armco barrier and broke in half, leaving Ahrens strapped in the back. Kurt Ahrens Jr. profile at The 500 Owners Association

Leo Deutsch

Lev Grigorievich Deutsch known as Leo Deutsch was a Russian Marxist revolutionary and one of four founding members of Russia's Marxist Organisation, the precursor of the Russian Social Democratic Labour Party. Lev Grigorievich Deutsch was born September 25, 1855 in Tulchyn, the son of a Jewish merchant father and a peasant mother. At the age of 19, he joined a Narodnik group in Kiev, took part in the'to the people' movement, in which young radicals dressed as peasants, went to villages to spread socialist ideas, he avoided arrest, unlike many of the participants, but returned, disillusioned in the summer of 1875 and volunteered to join the infantry, hoping to be sent to the Balkans to fight the Turks, but in February 1876, he was implicated in helping a revolutionary named Semyon Lurie, one of the defendants at the Trial of the 193 to escape from Kiev prison, deserted, to avoid a court martial. He joined an illegal group known as the Kiev buntari. In June 1876, Deutsch was living illegally in Elisavetgrad when a former student named Gorinovich sought to join his group.

Gorinovich had been arrested for taking part in the'to the people' movement in 1874, but was released. Deutsch believed that he had gained his release by denouncing others, was an active police spy, resolved to kill him, he and a fellow revolutionary, V. A. Malinka, persuaded Gorinovich to join them on a trip to Odessa, on the way attacked him and left him for dead, though he recovered and named his attackers. Malinka was hanged for his part in attack in December 1878; this was the first act of violence committed by Russian revolutionaries during the 1870s, made Deutsch so notorious that when a young Jewish woman was arrested as one of the conspirators who had assassinated the Tsar Alexander II in 1881, the Russian press wrongly assumed that she was Deutsch's sister. In summer 1877, he was arrested as an accomplice of Yakov Stefanovich in the Chigirin Affair and held in Kiev prison, but both men escaped in May 1878 after a fellow revolutionary, Mikhail Frolenko, had obtained a post as a prison warden and let them out one night.

Deutsch escaped to Europe, but returned to St Petersburg, - despite his past record - was a founding member of Chornyi peredel, rather than the more violent and conspiratorial People's Will, who carried out the assassination of the Tsar. In 1880 Deutsch and other leaders of the Black Repartition group, including George Plekhanov, Vera Zasulich and Pavel Axelrod emigrated to Geneva. Abroad, Plekhanov studied the works of Karl Marx, persuaded the other three to join him in 1883 in creating the marxist Emancipation of Labour. All Russia's marxist parties, including the Communist Party, traced their lineage from this group; as its most experienced illegal operator, Deutsch was put in charge of smuggling Marxist literature into Russia, but was arrested in Germany in March 1884. It was rare for Russian revolutionaries to be extradited by any European government, but Deutsch was treated as a common criminal because the attempt to kill Gorinovich, sent back to St Petersburg in a cattle truck. At this trial, he admitted the offence, but was denied the right to explain his reasons for it, was sentenced to 13 years and four months in prison.

In 1890, he was deported to the Kara region of Siberia, where he was shared a cell with other political revolutionaries. According to his account, when Deutsch told them that he had become a Marxist - an ideology little known outside Germany - "Had I announced myself a follower of the prophet Mohammed, they could scarcely have been more surprised." In 1900, Deutsch made a dramatic escape from Siberia, through Japan, the USA, Liverpool and Paris, to rejoin the Emancipation of Labour League in Switzerland in November 1901. His three former comrades there had since joined Vladimir Lenin, Julius Martov, Alexander Potresov on the six-member editorial board of the newspaper Iskra, riven by rivalry between the generations. Plekhanov hoped that Deutsch would take over the task of smuggling the paper into Russia from Lenin, putting the older revolutionaries back in control of the project, but his long imprisonment had taken too much of a toll for him to assume the task. Deutsch was present as an observer at the second congress of the Russian Social Democratic Labour Party in 1903 when it split into its Bolshevik and Menshevik factions.

He sided the Mensheviks - Martov, Zasulich, Leon Trotsky et al. Lenin's widow recalled incident involving Deutsch, a Bolshevik named Vladimir Noskov, as the conference was ending: "Deutsch was angrily reprimanding'Glebov' about something; the latter raised his head and with gleaming eyes said bitterly:'You just keep your mouth shut, you old dodderer!'"During the 1905 Revolution Deutsch returned to Russia but was arrested and imprisoned. However, on the way to Siberia he escaped and made his way to London, starting a period of foreign exile which lasted until the February 1917 Russian Revolution. From October 1915 to September 1916, Deutsch edited a monthly newspaper in New York City called Svobodnoe Slovo. In 1917, Deutsch joined George Plekhanov in editing Edinstvo, he wrote his memoirs and edited a volume of documents associated with the Emancipation of Labour group. Deutsch died on August 5, 1941. Deutsch never married, though his memoirs show that he had friendly and affectionate relations with the wives of other revolutionaries, such as Pavel Axelrod.

It is probable that he was gay, though he may not have been homosexual. During his imprisonment exile in Kara, he and Yakov Stefanovitch - the only exile ready to listen sympathetically to Deutsch's reasons for con

Yulian Panich

Yulian Aleksandrovich Panich is a Soviet / Russian actor and journalist. Honored Artist of Russia. After graduating from the Shchukin Acting School in Moscow in 1954, Panich had a successful career of a Soviet film actor. In 1965 began working as a television and film director. In 1972, Yulian Panich left the Soviet Union for Israel; that year he was offered a job in Munich with the Radio Liberty/Free Europe radio. Soon Panich became chief program producer with the Russian service and the symbol of anti-Soviet resistance; as such he was the object of special interest by the KGB. After his retirement in 1995, Yulian Panich had been living in the suburbs of Paris - Rambouillet. Yulian Panich is married to Ludmila Zweig since 1956, they have a son, Igor Panich, a writer. Road to Life as Semyon For the Power of the Soviets as Svyatoslav Marchenko Bloody Dawn as Marco Hushcha Different Fates as Fedor Morozov Three Hundred Years Ago... as Tymofiy Khmelnytsky Total Expensive as Roman Baklanov Leningrad Symphony as episode Stepan Kolchugin as Kuzma Kochubey as Sashko Nalivayko About my Friend as Aram Carefully, Grandma! as Vasya Kazatchkov Reflections as episode Novels Red House as Maxim Sivoshapko Green Coach as Prince Vasili Pervorossiyane as Ataman Shurakov Seeing the White Nights as director Yulian Panich on IMDb Юлиан Панич.

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