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Zero divisor

In abstract algebra, an element a of a ring R is called a left zero divisor if there exists a nonzero x such that ax = 0, or equivalently if the map from R to R that sends x to ax is not injective. An element a of a ring is called a right zero divisor if there exists a nonzero y such that ya = 0; this is a partial case of divisibility in rings. An element, a left or a right zero divisor is called a zero divisor. An element a, both a left and a right zero divisor is called a two-sided zero divisor. If the ring is commutative the left and right zero divisors are the same. An element of a ring, not a left zero divisor is called left regular or left cancellable. An element of a ring, not a right zero divisor is called right regular or right cancellable. An element of a ring, left and right cancellable, is hence not a zero divisor, is called regular or cancellable, or a non-zero-divisor. A zero divisor, nonzero is called a nonzero zero divisor or a nontrivial zero divisor. If there are no nontrivial zero divisors in R R is a domain.

In the ring Z / 4 Z, the residue class 2 ¯ is a zero divisor since 2 ¯ × 2 ¯ = 4 ¯ = 0 ¯. The only zero divisor of the ring Z of integers is 0. A nilpotent element of a nonzero ring is always a two-sided zero divisor. An idempotent element e ≠ 1 of a ring is always a two-sided zero divisor, since e = 0 = e; the ring of n × n matrices over a field has nonzero zero divisors if n ≥ 2. Examples of zero divisors in the ring of 2 × 2 matrices are shown here: = =, = =. A direct product of two or more nonzero rings always has nonzero zero divisors. For example, in R 1 × R 2 with each R i nonzero, =, so is a zero divisor. Consider the ring of matrices with x, z ∈ Z and y ∈ Z / 2 Z. = and ( x y

Journeymen Tailors Union

The Journeymen Tailors Union was a trade union in the United States, with some local branches in Canada. Forerunners to the organization included the Tailors Progressive Union of America in the mid-1800s, as well as assemblies organized by the Knights of Labor. Important was the tension between custom tailors and shop tailors. Regardless, there was little to no significant and unified tailors' union or movement before the 1880s. By shop tailors had begun to build more sophisticated organizations, which were joined by custom tailors, a move, vocally supported by John Brown Lennon, the future general secretary of the Journeymen Tailors' Union. A critical concern was the scabbing of custom tailors on shop tailors and vice versa during strikes, which could only be prevented by a more unified form of organization. John Brown Lennon became general secretary in 1886, a position he would hold until losing it to the Canadian socialist Eugene Brais in 1910. By 1887, the Tailors' Progressive Union had adopted a union label to be affixed to clothing, recognized by the American Federation of Labor.

The JTU followed with its own union label in 1891. The TPUA was more integrated into the labour movement, being composed of shop tailors, many of whom were outspoken socialists and saw a common cause with other workers more than the journeymen custom tailors did. After 1889, the TPUA had declined in importance and attempts were made by shop tailors to join the JTU, which were rebuffed. In response, some shop tailors and other ready-made clothing workers started the United Garment Workers of America in 1891 and the International Ladies' Garment Workers Union in 1900. All three organizations were recognized by the AFL; these clashes resulted in victory for the UGWA and diminished importance for the JTU, with the UGWA gaining jurisdiction over all non-custom-made clothing manufacture, with the JTU being limited to custom tailoring establishments, despite the wishes of its then-secretary, John Brown Lennon. In 1897, the JTU lost jurisdiction over special-order custom tailoring to the UGWA and Custom Clothing Makers' Union or Special Order Clothing Makers' Union, whose AFL charter was denied.

After 1900, successive and nearly annual attempts to reform the organization, to extend its jurisdiction, in 1905 to merge with the UGWA and form a Garment Workers' and Tailors' International Union, all failed by membership vote. At its convention in Buffalo in 1909, the JTU recognized the rise in custom factory tailoring at the expense of old-style merchant tailoring, as a result it claimed jurisdiction over all custom tailoring, ineffectually enforced and never backed by the AFL; as a result, the JTU began to engage in "raiding" by attempting to organize workers claimed under the jurisdiction of the UGWA. With Lennon's attempts to amalgamate the organization with the UGWA and ILGWU failed and Eugene Brais elected as secretary, the direction of the organization changed drastically, with the rising socialist wing taking de facto control and renaming the organization to the International Tailors' Industrial Union, articulating their preference for industrial unionism over craft unionism and putting it at odds Samuel Gompers, the president of the AFL and a personal friend of John Brown Lennon, who accused the JTU/TIUI of violating AFL bylaws by changing its name without permission.

By the early 1910s, the union was divided into three factions: "old party", "progressives", "liberals", the latter of which advocated reform but retention of the trade union model. This was similar to other garment workers unions, which saw surging support for socialist and industrial unionist positions and within the UGWA, an embrace of class struggle politics; this reflected broad trends at the time which were exemplified by the rise of purely industrial unionist and anti-capitalist organizations such as the Industrial Workers of the World. In 1914, a faction of disaffected UGWA members led by Sidney Hillman split from the organization and joined the JTU/TIUI instead, which by December had passed a motion proposing to rename the organization the Amalgamated Clothing Workers of America in preparation for a merger with the Hillman faction. Passed was a motion barring members from belonging in two unions of the same trade, a gambit to force the Hillman faction into the JTU/TIUI/ACWA camp; the merger was defeated by vote and further propositions returned the name to "Journeyman Tailors' Union of America", a move which led to congratulations from the leadership of the AFL.

John Brown Lennon, 1886-1909 Eugene J. Brais, 1910-1915 Thomas Sweeney, 1917 Archival copies of The Tailor, the JTU's official publication

John Douglas (sportsman)

John Raymond Douglas is a former Australian sportsman who played Australian rules football in the Victorian Football League with North Melbourne during the 1970s and first-class cricket for Victoria. From the Coburg Amateurs Douglas made his VFL debut in the opening round of the 1972 season against St Kilda, whose Brownlow Medal rover Ross Smith was celebrating his 200th game, he played six further games that year and did not appear again until 1975, when North Melbourne won their inaugural premiership with Douglas taking the field three times during the home and away season. He finished his football career after playing just two games in 1976, to finish with 12 games and eight goals for North Melbourne. A right-arm fast-medium pace bowler, Douglas claimed 30 wickets at 26.53 from his nine first-class matches. The first lot of matches came during the summer of 1975/76, while he was still a North Melbourne player, beginning with a Sheffield Shield encounter against New South Wales. Test player John Dyson was his maiden wicket and he finished his first innings with 4/65.

In early 1976, Douglas toured South Africa with the DH Robins' XI, a team with first-class status who annually toured the country during apartheid. His wickets for the tour included Barry Richards; the rest of his first-class matches were for Victoria in the Sheffield Shield, the most memorable being against South Australia at Adelaide Oval when he took match figures of 11/138. The haul included his best innings figures of 7/71. List of Victoria first-class cricketers John Douglas's playing statistics from AFL Tables Cricinfo: John Douglas

Big & Beautiful

Big & Beautiful is the third studio album by hip hop group The Fat Boys, released in May 1986 through Sutra Records. "Sex Machine" – 4:46 "Go For It" – 4:33 "Breakdown" – 4:12 "Double-O Fat Boys" – 5:01 "Big & Beautiful" – 4:25 "Rapp Symphony" – 4:01 "Human Beat Box, Part III" – 4:12 "In The House" – 4:12 "Beat Box Is Rockin'" – 3:36 Musicians: Fresh Gordon, Doug Grama, Jeff Johnson, Mark Morales, Dave Ogrin, Darren Robinson, Gary Rottger Background vocals: Peter Lewis, Cindy Mizelle, Peter Sturge, Audrey Wheeler, Alyson Williams Recording and mixing engineers: Doug Grama, Dave Ogrin, Bobby Di Riso Mastering: Frankford/Wayne Mastering Labs Executive producer: Charles Stettler Photography: Howard Menken Design: Lynda West Singles The Fat Boys-Big & Beautiful at Discogs

Sperry, Oklahoma

Sperry is a town in Tulsa County, United States. The population was 1,205 in the 2010 U. S. census, compared to 1,351 at the 2000 census. It is a bedroom community since about 85 percent of the employed residents commute to work in Tulsa and other nearby towns. Sperry has an active retirement community. Native American activity in the area predates the establishment of the town. Of note during the American Civil War was the Battle of Chusto-Talasah about 9 miles southeast on the “Caving Banks” bend of Bird Creek, where on December 9, 1861, Opothleyahola’s Union-allied Indians met the forces of Col. D. H. Cooper’s Confederate troops. Sperry was known as Beuhler Switch, it was named after an employee of the Midland Valley Railroad. The Sperry post office in the Cherokee Nation was established on May 17, 1902 to serve a rural community between Hominy and Delaware Creeks; the post office was located in the Carson Ranch house. The origin of the name Sperry is not clear. One source claims that the name was derived from the surname of a local landowner named Henry Spybuck.

The Midland Valley Railroad built a line from Arkansas to Eastern Kansas that reached Sperry in March 1905. The route no longer exists, but has been converted from rail into the 14.5 mile Osage Prairie Trail linking Sperry with Tulsa to the south and Skiatook to the north. Exploration for oil brought prosperity between 1905 and 1910. Sperry incorporated in 1920, when the census recorded a population of 487. Two communities joined to form present-day Sperry. One was known as "Buehler Switch." This was the larger community, the location of the railroad and depot, centered around 96th Street North and S. H. 11. The smaller community, consisting of only two or three homes and a general store/post office housed in the same building, was known as Sperry, it was on Hominy Creek near 106th Street North Peoria. When statehood occurred in 1907, the post office was renamed Sperry and was moved from the general store to a new grocery store near the depot. From 1982 to 1989, the Sperry WPA armory served as headquarters to the newly organized Oklahoma Army National Guard 45th Special Operations Aviation Regiment.

The "Lords of Darkness" specialized in operating the OH-6 Little Bird helicopter while using night vision goggles. Aircraft were kept a short distance from the Tulsa Air National Guard Base; the unit evolved into the 1-245th Aviation Regiment, now housed at the Tulsa Army National Guard Aviation Complex near 46th St N and Highway 169, built 1988. Sperry is located at 36°17′43″N 95°59′24″W, it is about 10 miles north of downtown Tulsa. According to the United States Census Bureau, the town has a total area of 0.9 square miles, all of it land. As of the census of 2000, there were 1,351 people, 375 households, 78 families residing in the town; the population density was 1,118.3 people per square mile. There were 406 housing units at an average density of 462.8 per square mile. The racial makeup of the town was 70.64% White, 0.51% African American, 18.86% Native American, 0.10% Asian, 1.94% from other races, 7.95% from two or more races. Hispanic or Latino of any race were 2.75% of the population. There were 375 households out of which 36.8% had children under the age of 18 living with them, 49.1% were married couples living together, 17.6% had a female householder with no husband present, 28.3% were non-families.

25.3% of all households were made up of individuals and 13.3% had someone living alone, 65 years of age or older. The average household size was 2.60 and the average family size was 3.14. In the town, the population was spread out with 30.7% under the age of 18, 9.5% from 18 to 24, 25.2% from 25 to 44, 21.5% from 45 to 64, 13.1% who were 65 years of age or older. The median age was 34 years. For every 100 females, there were 92.0 males. For every 100 females age 18 and over, there were 86.3 males. The median income for a household in the town was $26,713, the median income for a family was $30,192. Males had a median income of $26,167 versus $18,542 for females; the per capita income for the town was $11,767. About 15.1% of families and 89.2% of the population were below the poverty line, including 26.9% of those under age 18 and 12.9% of those age 65 or over. Sperry Public Schools is an independent school district in Sperry, Oklahoma serving grades K-12; the Elementary and High School buildings share a campus on the western edge of Sperry

Nannophrys ceylonensis

Nannophrys ceylonensis known as the Sri Lanka rock frog or the Ceylon streamlined frog, is a species of frog. It used to be placed in the large frog family Ranidae but a phylogenetic study was undertaken using DNA sequences and it is now included in the family Dicroglossidae, it is endemic to Sri Lanka where its natural habitats are subtropical or tropical moist lowland forests, subtropical or tropical moist montane forests and streams. Female Sri Lanka rock frogs grow to a length of about 5 centimetres while males grow to 4 centimetres; the colour is olive yellowish-brown, mottled with brown patches. The legs have transverse bars of brown; when sitting on alga covered rocks it is well camouflaged. The Sri Lanka rock frog is endemic to south and western Sri Lanka where it is found in wet tropical forests at altitudes of up to 1,200 metres above sea level, it is a aquatic species and occurs in fast flowing mountain streams, under boulders and on wet rocks beside waterfalls. It is found on land in disturbed areas where there are suitable breeding locations such as wet seeps.

The tadpoles are sometimes found on wet rocks beside torrents. The female Sri Lanka rock frog spawns a cluster of eggs in a crevice in the splash zone of a mountain stream; the male frog guards the eggs in several nests and ensures that they are kept moist while the female plays no further part in parental care. The eggs hatch into tadpoles that forage for small invertebrates on the surface of the rocks near their nest. In the IUCN Red List of Threatened Species, Nannophrys ceylonensis is listed as Vulnerable; this is because numbers seem to be declining and it has several disjunct populations, the total area of its range being less than 2,000 square kilometres. The streams in which it lives and breeds are subject to pollution by agrochemicals and the volume of water is reduced during periods of drought