About: Rng (algebra)

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In mathematics, and more specifically in abstract algebra, a pseudo-ring is one of the following variants of a ring: * A rng, i.e., a structure satisfying all the axioms of a ring except for the existence of a multiplicative identity. * A set R with two binary operations + and ⋅ such that (R, +) is an abelian group with identity 0, and a(b + c) + a0 = ab + ac and (b + c)a + 0a = ba + ca for all a, b, c in R. * An abelian group (A, +) equipped with a subgroup B and a multiplication B × A → A making B a ring and A a B-module.

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rdfs:label	Pseudo-ring (en)
rdfs:comment	In mathematics, and more specifically in abstract algebra, a pseudo-ring is one of the following variants of a ring: * A rng, i.e., a structure satisfying all the axioms of a ring except for the existence of a multiplicative identity. * A set R with two binary operations + and ⋅ such that (R, +) is an abelian group with identity 0, and a(b + c) + a0 = ab + ac and (b + c)a + 0a = ba + ca for all a, b, c in R. * An abelian group (A, +) equipped with a subgroup B and a multiplication B × A → A making B a ring and A a B-module. (en)
dcterms:subject	Algebras Ring theory Algebraic structures
Wikipage page ID	51508407 (xsd:integer)
Wikipage revision ID	1071304946 (xsd:integer)
Link from a Wikipage to another Wikipage	Module (mathematics) Rng (algebra) Algebras Ring theory Mathematics Multiplicative identity Subgroup Additive identity Algebraic structures Ring (mathematics) Abelian group Abstract algebra Binary operation Axiom Semiring
sameAs	Rng (algebra) Rng (algebra) Rng (algebra) Rng (algebra)
dbp:wikiPageUsesTemplate	dbt:Algebra-stub dbt:Reflist
has abstract	In mathematics, and more specifically in abstract algebra, a pseudo-ring is one of the following variants of a ring: * A rng, i.e., a structure satisfying all the axioms of a ring except for the existence of a multiplicative identity. * A set R with two binary operations + and ⋅ such that (R, +) is an abelian group with identity 0, and a(b + c) + a0 = ab + ac and (b + c)a + 0a = ba + ca for all a, b, c in R. * An abelian group (A, +) equipped with a subgroup B and a multiplication B × A → A making B a ring and A a B-module. None of these definitions are equivalent, so it is best to avoid the term "pseudo-ring" or to clarify which meaning is intended. (en)
prov:wasDerivedFrom	wikipedia-en:Pseudo-ring?oldid=1071304946&ns=0
page length (characters) of wiki page	1861 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Pseudo-ring
is Link from a Wikipage to another Wikipage of	Rng (algebra) Proofs of elementary ring properties Null ideal Identity element Krull's theorem Pseudoring
is Wikipage redirect of	Pseudoring
is foaf:primaryTopic of	wikipedia-en:Pseudo-ring

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