Abelian
In mathematics, Abelian refers to any of number of different mathematical concepts named after Niels Henrik Abel:
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Some articles on abelian:
Pseudo-abelian Category
... In mathematics, specifically in category theory, a pseudo-abelian category is a category that is preadditive and is such that every idempotent has a kernel ... The pseudo-abelian condition is stronger than preadditivity, but it is weaker than the requirement that every morphism have a kernel and cokernel, as is true for ... Synonyms in the literature for pseudo-abelian include pseudoabelian and Karoubian ...
... In mathematics, specifically in category theory, a pseudo-abelian category is a category that is preadditive and is such that every idempotent has a kernel ... The pseudo-abelian condition is stronger than preadditivity, but it is weaker than the requirement that every morphism have a kernel and cokernel, as is true for ... Synonyms in the literature for pseudo-abelian include pseudoabelian and Karoubian ...
Associated Prime - Examples
... If R is the ring of integers, then non-trivial free abelian groups and non-trivial abelian groups of prime power order are coprimary ... If R is the ring of integers and M a finite abelian group, then the associated primes of M are exactly the primes dividing the order of M ...
... If R is the ring of integers, then non-trivial free abelian groups and non-trivial abelian groups of prime power order are coprimary ... If R is the ring of integers and M a finite abelian group, then the associated primes of M are exactly the primes dividing the order of M ...
Pseudo-abelian Category - Examples
... Any abelian category, in particular the category Ab of abelian groups, is pseudo-abelian ... Indeed, in an abelian category, every morphism has a kernel ... category of associative rngs (not rings!) together with multiplicative morphisms is pseudo-abelian ...
... Any abelian category, in particular the category Ab of abelian groups, is pseudo-abelian ... Indeed, in an abelian category, every morphism has a kernel ... category of associative rngs (not rings!) together with multiplicative morphisms is pseudo-abelian ...
Abelian - Other Uses
... Abelians, 4th-century Christian sect Hovhannes Abelian (1865–1936), Armenian actor ...
... Abelians, 4th-century Christian sect Hovhannes Abelian (1865–1936), Armenian actor ...
Surgery Exact Sequence - Versions Revisited
... This is achieved by putting an alternative abelian group structure on the normal invariants as described here ... with the algebraic surgery exact sequence of Ranicki which is an exact sequence of abelian groups by definition ... This gives the structure set the structure of an abelian group ...
... This is achieved by putting an alternative abelian group structure on the normal invariants as described here ... with the algebraic surgery exact sequence of Ranicki which is an exact sequence of abelian groups by definition ... This gives the structure set the structure of an abelian group ...
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