MathGloss

Let $A$ and $B$ be two algebras over the same field (or commutative ring) $K$. Then an algebra homomorphism between $A$ and $B$ is a map $f:A\to B$ such that

1. $f(kx) = kf(x)$
2. $f(x+y) = f(x) + f(y)$
3. $f(xy) = f(x)f(y)$ for all $k\in K$ and $x,y\in A$.

If an algebra homomorphism is bijective, then it is an isomorphism of algebras.

Wikidata ID: Q382497

This site is open source. Improve this page.