The Church of Sweden is an Evangelical Lutheran national church in Sweden. A former state church, headquartered in Uppsala, with 5.9 million members at year end 2018 it is the largest Christian denomination in Sweden. It is the largest Lutheran denomination in Europe and the third-largest in the world after the Ethiopian Evangelical Church Mekane Yesus and the Evangelical Lutheran Church in Tanzania. A member of the Porvoo Communion, the Church professes the Lutheran branch of Christianity, it is composed of thirteen dioceses, divided into parishes. It is an open national church which, working with a democratic organisation and through the ministry of the church, covers the whole nation; the Primate of the Church of Sweden is the Archbishop of Uppsala — Antje Jackelén, Sweden's first female archbishop. Today, the Church of Sweden is an Evangelical Lutheran church, it is liturgically and theologically "high church", having retained priests and the Mass during the Swedish Reformation. In common with other Evangelical Lutheran churches, the Church of Sweden maintains the historical episcopate.

Some Lutheran churches have congregational polity or modified episcopal polity without Apostolic succession, but the historic episcopate is maintained in Sweden and the other Lutheran nations of the Porvoo Communion. The Church of Sweden is known today for its liberal position in theological issues the question of homosexuality; when Eva Brunne was consecrated as Bishop of Stockholm in 2009, she became the first lesbian bishop in the world. Despite a significant yearly loss of members, its membership of 5,899,242 people accounts for 57.7% of the Swedish population. Until 2000 it held the position of state church; the high membership numbers are because until 1996 all newborn children were made members, unless their parents had cancelled their membership. 2% of the church's members attend Sunday services. According to a Gallup poll conducted in 2009, 17% of the Swedish population considered religion as an important part of their daily life. King Gustav I Vasa instigated the Church of Sweden in 1536 during his reign as King of Sweden.

This act separated the church from its canon law. In 1571, the Swedish Church Ordinance became the first Swedish church order following the Reformation; the Church of Sweden became Lutheran at the Uppsala Synod in 1593 when it adopted the Augsburg Confession to which most Lutherans adhere. At this synod, it was decided that the church would retain the three original Christian creeds: the Apostles', the Athanasian, the Nicene. In 1686, the Riksdag of the Estates adopted the Book of Concord, although only certain parts, labelled Confessio fidei, were considered binding, the other texts explanatory. Confessio dei included the three aforementioned Creeds, the Augsburg Confession and two Uppsala Synod decisions from 1572 and 1593. During the 19th and 20th centuries, a variety of teachings were approved directed towards ecumenism: 1878 development of the Catechism the Uppsala Creed of 1909, preparing for Eucharistic communion with the Church of England the constitutions of World Council of Churches the constitutions of Lutheran World Federation Church of Sweden's official response to the "Lima document" a Council of the Bishops Letter in Important Theological Questions the 1995 Treaty of Communion with the Philippine Independent ChurchIn practice, the Lutheran creed texts play a minor role, instead the parishes rely on Lutheran tradition in coexistence with influences from other Christian denominations and diverse ecclesial movements such as Low Church, High Church and Laestadianism, which locally might be established, but which have little nationwide influence.

During the 20th century the Church of Sweden oriented itself towards liberal Christianity and human rights. In 1957, the church assembly rejected a proposal for ordination of women, but the Riksdag changed the law in spring 1958 and forced the church assembly to accept the new law in autumn 1958. Since 1960, women have been ordained as priests, since 1994, men who oppose collaboration with women priests have not been allowed ordination. A proposal to perform same-sex weddings was approved on October 22, 2009 by 176 of 249 voting members of the Church of Sweden Synod. In 2000 the Church of Sweden ceased to be a state church, but there remains a strong tradition of community connection with churches in relation to rites of passage, with many infants baptized and teenagers confirmed for families without formal church membership. While some Swedish areas had Christian minorities in the 9th century, Sweden was, because of its geographical location in northernmost Europe, not Christianized until around AD 1000, around the same time as the other Nordic countries, when the Swedish King Olof was baptized.

This left only a modest gap between the Christianization of Scandinavia and the Great Schism, however there are some Scandinavian/Swedish saints who are venerated eagerly by many Orthodox Christians, such as St. Olaf. However, Norse paganism and other pre-Christian religious systems survived in the territory of what is now Sweden than that; the Christian church in Scandinavia was governed by the archdiocese of Bremen. In 1104 an archbishop for all Scandinavia was installed in Lund. Uppsala was ma

In mathematics, a unique factorization domain is a ring in which a statement analogous to the fundamental theorem of arithmetic holds. A UFD is an integral domain in which every non-zero non-unit element can be written as a product of prime elements, uniquely up to order and units. Important examples of UFDs are the integers and polynomial rings in one or more variables with coefficients coming from the integers or from a field. Unique factorization domains appear in the following chain of class inclusions: commutative rings ⊃ integral domains ⊃ integrally closed domains ⊃ GCD domains ⊃ unique factorization domains ⊃ principal ideal domains ⊃ Euclidean domains ⊃ fields ⊃ finite fields Formally, a unique factorization domain is defined to be an integral domain R in which every non-zero element x of R can be written as a product of irreducible elements pi of R and a unit u: x = u p1 p2 ⋅⋅⋅ pn with n ≥ 0and this representation is unique in the following sense: If q1... qm are irreducible elements of R and w is a unit such that x = w q1 q2 ⋅⋅⋅ qm with m ≥ 0,then m = n, there exists a bijective map φ: → such that pi is associated to qφ for i ∈.

The uniqueness part is hard to verify, why the following equivalent definition is useful: A unique factorization domain is an integral domain R in which every non-zero element can be written as a product of a unit and prime elements of R. Most rings familiar from elementary mathematics are UFDs: All principal ideal domains, hence all Euclidean domains, are UFDs. In particular, the integers, the Gaussian integers and the Eisenstein integers are UFDs. If R is a UFD so is R, the ring of polynomials with coefficients in R. Unless R is a field, R is not a principal ideal domain. By induction, a polynomial ring in any number of variables over any UFD is a UFD; the formal power series ring K over a field K is a UFD. On the other hand, the formal power series ring over a UFD need not be a UFD if the UFD is local. For example, if R is the localization of k/ at the prime ideal R is a local ring, a UFD, but the formal power series ring R over R is not a UFD; the Auslander–Buchsbaum theorem states that every regular local ring is a UFD.

Z is a UFD for all integers 1 ≤ n ≤ 22, but not for n = 23. Mori showed that if the completion of a Zariski ring, such as a Noetherian local ring, is a UFD the ring is a UFD; the converse of this is not true: there are Noetherian local rings that are UFDs but whose completions are not. The question of when this happens is rather subtle: for example, for the localization of k/ at the prime ideal, both the local ring and its completion are UFDs, but in the similar example of the localization of k/ at the prime ideal the local ring is a UFD but its completion is not. Let R be any field of characteristic not 2. Klein and Nagata showed that the ring R/Q is a UFD whenever Q is a nonsingular quadratic form in the X's and n is at least 5; when n=4 the ring need not be a UFD. For example, R / is not a UFD, because the element X Y equals the element Z W so that X Y and Z W are two different factorizations of the same element into irreducibles; the ring Q / is a UFD. On the other hand, The ring Q / is not a UFD.

The coordinate ring R/ of the 2-dimensional real sphere is a UFD, but the coordinate ring C/ of the complex sphere is not. Suppose that the variables Xi are given weights wi, F is a homogeneous polynomial of weight w. If c is coprime to w and R is a UFD and either every finitely generated projective module over R is free or c is 1 mod w, the ring R/ is a UFD; the quadratic integer ring Z of all complex numbers of the form a + b − 5, where a and b are integers, is not a UFD because 6 factors as both 2×3 and as. These are different factorizations, because the only units in this ring are 1 and −1, it is not hard

Barbery is a commune in the Calvados department in the Normandy region of north-western France. The inhabitants of the commune are known as Barberigeoises. Barbery is located some 18 km south by south-east of Caen and 10 km east by north-east of Thury-Harcourt. Access to the commune is by the D131 road from Croisilles in the south-west which passes through the heart of the commune and the village before continuing north-east to Urville; the D23 comes from Cesny-Bois-Halbout in the south and passes through the village before continuing north to join Route nationale N158 at Saint-Aignan-de-Cramesnil. The D156A goes south-east from the village to Moulines; the D237 branches off the D131 in the east of the commune and goes south-east to join the D167 east of the commune. Apart from the village there are the hamlets of L'Abbaye, Faverolles, Le Londel, Le Mesnil Touffray; the commune is farmland. The Ruisseau du Val Clair rises north of the village and flows north to join the Laize at Bretteville-sur-Laize.

The Ruisseau de Corneville rises north of the village, east of the Ruisseau du Val Clair, flows north to join the Laize at Les Écluses. During early medieval times Barbery and its abbey were under the control of the de Livet family. Barbery appears as the same on the 1790 version. List of Successive Mayors; the evolution of the number of inhabitants is known from the population censuses conducted in the commune since 1793. From the 21st century, a census of communes with fewer than 10,000 inhabitants is held every five years, unlike larger communes that have a sample survey every year; the commune has many buildings and sites that are registered as historical monuments: The Petite-Abbaye Industrial Cheese Factory Farmhouses A Chateau at Mesnil-Aumont A Manor/Chateau at Mesnil-Touffray The Old Abbey Manor at Faverolles The commune has several religious buildings and structures that are registered as historical monuments: The old Cistercian Abbey of Notre-Dame of Barbery founded by Robert Marmion in 1181.

The Parish Church of Saint Peter. The Church contains many items that are registered as historical objects: Statues A green Sofa, 2 Chairs A Stoup A Baptismal font An Altar and Tabernacle 4 Stained glass windows A Presbytery The Parish Church of Saint Martin at Mesnil-Touffray; the Church contains many items that are registered as historical objects: Statues A Pulpit A Baptismal font An Altar and Retable Tombstones A Monument to Charles de Lalongny Communes of the Calvados department