Algebra extension
id:
algebra-extension-176-1289960
title:
Algebra extension
text:
In abstract algebra, an algebra extension is the ring-theoretic equivalent of a group extension. Precisely, a ring extension of a ring R by an abelian group I is a pair (E, ϕ ) consisting of a ring E and a ring homomorphism ϕ that fits into the short exact sequence of abelian groups:
- 0 → I → E → ϕ R → 0. This makes I isomorphic to a two-sided ideal of E. Given a commutative ring A, an A-extension or an extension of an A-algebra is defined in the same way by replacing "ring" with "algebra ove
brand slug:
wiki
category slug:
encyclopedia
description:
Surjective ring homomorphism with a given codomain
original url:
https://en.wikipedia.org/wiki/Algebra_extension
date created:
2006-02-17T14:44:10Z
date modified:
2024-09-03T13:34:52Z
main entity:
{"identifier":"Q1166643","url":"https://www.wikidata.org/entity/Q1166643"}
image:
fields total:
13
integrity:
15