Ring extension

In commutative algebra, a ring extension is a ring homomorphism of commutative rings, which makes S an R-algebra. In this article, a ring extension of a ring R by an abelian group I is a pair of a ring E and a surjective ring homomorphism such that I is isomorphic (as an abelian group) to the kernel of In other words, is a short exact sequence of abelian groups. (This makes I a two-sided ideal of E.) Given a commutative ring A, an A-extension is defined in the same way by replacing "ring" with "algebra over A" and "abelian groups" with "A-modules".

Ring extension

In commutative algebra, a ring extension is a ring homomorphism of commutative rings, which makes S an R-algebra. In this article, a ring extension of a ring R by an abelian group I is a pair of a ring E and a surjective ring homomorphism such that I is isomorphic (as an abelian group) to the kernel of In other words, is a short exact sequence of abelian groups. (This makes I a two-sided ideal of E.) Given a commutative ring A, an A-extension is defined in the same way by replacing "ring" with "algebra over A" and "abelian groups" with "A-modules".