Definition:Basis of Module

Definition
Let $R$ be a ring with unity.

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

Also see

 * Equivalence of Definitions of Basis of Module
 * Definition:Free Module
 * Definition:Dimension of Free Module
 * Bases of Free Module have Equal Cardinality
 * Definition:Ordered Basis

Special cases

 * Definition:Basis of Vector Space