Definition:Unitary Module

Definition

Let $\left({R, +_R, \times_R}\right)$ be a ring with unity whose unity is $1_R$.

Let $\left({G, +_G}\right)$ be an abelian group.

Let $\left({G, +_G, \circ}\right)_R$ be a module over $R$.

Then $\left({G, +_G, \circ}\right)_R$ is a unitary module over $R$ or unitary $R$-module iff:

$(4): \quad \forall x \in G: 1_R \circ x = x$.

Also see

• Results about unitary modules can be found here.

Sources

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