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 {\displaystyle \phi } ) consisting of a ring E and a ring homomorphism ϕ {\displaystyle \phi } that fits into the short exact sequence of abelian groups: 0 → I → E → ϕ R → 0.
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 {\displaystyle \phi } ) consisting of a ring E and a ring homomorphism ϕ {\displaystyle \phi } that fits into the short exact sequence of abelian groups: 0 → I → E → ϕ R → 0.
Source: Wikipedia "Algebra extension" · CC BY-SA 4.0
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