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In mathematics, the endomorphisms of an abelian group X form a ring. This ring is called the endomorphism ring of X, denoted by End(X); the set of all homomorphisms of X into itself. Addition of endomorphisms arises naturally in a pointwise manner and multiplication via endomorphism composition. Using these operations, the set of endomorphisms of an abelian group forms a (unital) ring, with the zero map as additive identity and the identity map as multiplicative identity.

Attributes	Values
rdfs:label	Okruh endomorfismů (cs) Endomorphism ring (en) 自己準同型環 (ja) Endomorfismenring (nl) Pierścień endomorfizmów (pl) Endomorfiring (sv)
rdfs:comment	Okruh endomorfismů je matematická struktura z oboru abstraktní algebry. Jejími prvky jsou endomorfismy nějakého objektu (jiné struktury) a dvě operace – skládání endomorfismů tohoto objektu, která realizuje „násobení“, a původní operace sčítání na objektu, přičemž výsledná struktura splňuje axiomy okruhu. Nulovým prvkem je endomorfismus zobrazující vše na nulový prvek původní struktury a neutrálním prvkem vzhledem k „násobení“ je identita. Okruh endomorfismů bývá značen End(X), kde X je nahrazeno označením původní struktury. (cs) 抽象代数学において、アーベル群 X の自己準同型環（英: endomorphism ring）End(X) は、X からそれ自身への準同型写像（X 上の自己準同型）すべてからなる集合である。加法は（）で定義され、積は写像の合成で定義される。自己準同型環の元となる「準同型」が何を指すものかは文脈によって異なり、これは考えている対象の圏に依存する。その結果、自己準同型環は対象のいくつかの内在的な性質を受け継いでいる。自己準同型環はしばしばある環上の多元環（代数）であり、自己準同型多元環（英: endomorphism algebra; 自己準同型代数）とも呼ばれる。 (ja) In de algebra, een deelgebied van de wiskunde, bestaat de endomorfismenring van een abelse groep uit de endomorfismen van die groep. Deze endomorfismen vormen een ring, onder de elementsgewijze optelling en de functiecompositie als vermenigvuldiging. (nl) Pierścień endomorfizmów – pierścień skojarzony z pewnym rodzajem obiektów, który zawiera pewną informację o jego własnościach wewnętrznych. (pl) Inom matematiken är endomorfiringen av en abelsk grupp X, betecknad med End(X), mängden av alla homomorfier av X till sig själv. Additionen definieras som punktvis addition av funktioner och multiplikationen definieras som funktionssammansättning. (sv) In mathematics, the endomorphisms of an abelian group X form a ring. This ring is called the endomorphism ring of X, denoted by End(X); the set of all homomorphisms of X into itself. Addition of endomorphisms arises naturally in a pointwise manner and multiplication via endomorphism composition. Using these operations, the set of endomorphisms of an abelian group forms a (unital) ring, with the zero map as additive identity and the identity map as multiplicative identity. (en)
dcterms:subject	Module theory Ring theory Category theory
Wikipage page ID	59623 (xsd:integer)
Wikipage revision ID	1104382182 (xsd:integer)
Link from a Wikipage to another Wikipage	Module (mathematics) Non-commutative ring Algebra (ring theory) Algebra over a field Module theory Homomorphism Vector space Indecomposable module Injective module Ring theory Mathematics Endomorphism Function composition Morita equivalence Continuous module Progenerator Clean ring Commutative ring Identity element Matrix ring Additive identity Local ring Addison-Wesley Additive map Algebra over a ring Field (mathematics) Finitely generated module Projective module Ring (mathematics) Von Neumann regular ring Preadditive category Zero morphism Category theory Abelian group Module homomorphism Zero map Division ring Pointwise Free module Idempotent element (ring theory) Identity function Initial object Integer Associative Category (mathematics) Category of rings Semiprimary ring Cengage Learning Schur's lemma Near-ring Uniform module Semisimple module Simple module Identity map Composition length Uniserial module dbr:Discrete_module
Link from a Wikipage to an external page	https://books.google.com/books%3Fid=hQTvAAAAMAAJ&q=endomorphism+ring https://archive.org/details/foundationsofmod0003wisb/page/
sameAs	Endomorphism ring Endomorphism ring Endomorphism ring Endomorphism ring Endomorphism ring Endomorphism ring Endomorphism ring Endomorphism ring Endomorphism ring
dbp:wikiPageUsesTemplate	dbt:Springer dbt:Citation dbt:Sfn dbt:Short_description
id	p/e035610 (en)
title	Endomorphism ring (en)
has abstract	Okruh endomorfismů je matematická struktura z oboru abstraktní algebry. Jejími prvky jsou endomorfismy nějakého objektu (jiné struktury) a dvě operace – skládání endomorfismů tohoto objektu, která realizuje „násobení“, a původní operace sčítání na objektu, přičemž výsledná struktura splňuje axiomy okruhu. Nulovým prvkem je endomorfismus zobrazující vše na nulový prvek původní struktury a neutrálním prvkem vzhledem k „násobení“ je identita. Okruh endomorfismů bývá značen End(X), kde X je nahrazeno označením původní struktury. (cs) In mathematics, the endomorphisms of an abelian group X form a ring. This ring is called the endomorphism ring of X, denoted by End(X); the set of all homomorphisms of X into itself. Addition of endomorphisms arises naturally in a pointwise manner and multiplication via endomorphism composition. Using these operations, the set of endomorphisms of an abelian group forms a (unital) ring, with the zero map as additive identity and the identity map as multiplicative identity. The functions involved are restricted to what is defined as a homomorphism in the context, which depends upon the category of the object under consideration. The endomorphism ring consequently encodes several internal properties of the object. As the resulting object is often an algebra over some ring R, this may also be called the endomorphism algebra. An abelian group is the same thing as a module over the ring of integers, which is the initial object in the category of rings. In a similar fashion, if R is any commutative ring, the endomorphisms of an R-module form an algebra over R by the same axioms and derivation. In particular, if R is a field F, its modules M are vector spaces V and their endomorphism rings are algebras over the field F. (en) 抽象代数学において、アーベル群 X の自己準同型環（英: endomorphism ring）End(X) は、X からそれ自身への準同型写像（X 上の自己準同型）すべてからなる集合である。加法は（）で定義され、積は写像の合成で定義される。自己準同型環の元となる「準同型」が何を指すものかは文脈によって異なり、これは考えている対象の圏に依存する。その結果、自己準同型環は対象のいくつかの内在的な性質を受け継いでいる。自己準同型環はしばしばある環上の多元環（代数）であり、自己準同型多元環（英: endomorphism algebra; 自己準同型代数）とも呼ばれる。 (ja) In de algebra, een deelgebied van de wiskunde, bestaat de endomorfismenring van een abelse groep uit de endomorfismen van die groep. Deze endomorfismen vormen een ring, onder de elementsgewijze optelling en de functiecompositie als vermenigvuldiging. (nl) Pierścień endomorfizmów – pierścień skojarzony z pewnym rodzajem obiektów, który zawiera pewną informację o jego własnościach wewnętrznych. (pl) Inom matematiken är endomorfiringen av en abelsk grupp X, betecknad med End(X), mängden av alla homomorfier av X till sig själv. Additionen definieras som punktvis addition av funktioner och multiplikationen definieras som funktionssammansättning. (sv)
gold:hypernym	Set
prov:wasDerivedFrom	wikipedia-en:Endomorphism_ring?oldid=1104382182&ns=0
page length (characters) of wiki page	8828 (xsd:nonNegativeInteger)

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