Category:Definitions/R-Algebraic Structures

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

Let $\struct {R, +_R, \times_R}$ be a ring.

Let $\struct {S, \ast_1, \ast_2, \ldots, \ast_n}$ be an algebraic structure with $n$ operations.

Let $\circ: R \times S \to S$ be a binary operation.

Then $\struct {S, \ast_1, \ast_2, \ldots, \ast_n, \circ}_R$ is an $R$-algebraic structure with $n$ operations.