Category:Definitions/R-Algebraic Structure Isomorphisms

This category contains definitions related to R-Algebraic Structure Isomorphisms.
Related results can be found in Category:R-Algebraic Structure Isomorphisms.

Let $\struct {S, \ast_1, \ast_2, \ldots, \ast_n, \circ}_R$ and $\struct {T, \odot_1, \odot_2, \ldots, \odot_n, \otimes}_R$ be $R$-algebraic structures.

Let $\phi: S \to T$ be an $R$-algebraic structure homomorphism.

Then $\phi$ is an $R$-algebraic structure isomorphism if and only if $\phi$ is a bijection.