Category:Definitions/Algebra Isomorphisms

This category contains definitions related to Algebra Isomorphisms.
Related results can be found in Category:Algebra Isomorphisms.

Let $R$ be a commutative ring.

Let $\struct {A, *}$ and $\struct {B, \times}$ be algebras over $R$.

Let $\phi: A \to B$ be an algebra homomorphism.

Then $\phi$ is an algebra isomorphism if and only if $\phi$ is a bijection.