Definition:R-Algebraic Structure Isomorphism

Definition

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

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

Then $\phi$ is an $R$-algebraic structure isomorphism iff $\phi$ is a bijection.

Note that this definition also applies to modules and also to vector spaces.

Also see

• Isomorphism (Abstract Algebra)

Sources

• Seth Warner: Modern Algebra (1965)... (previous)... (next): $\S 26$