Definition:Basis (Linear Algebra)

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

A basis of $$G$$ (plural: bases) is a linearly independent subset of $$G$$ which is a generator for $$G$$.

Comment
The pronunciation of bases in this context is bay-seez, not bay-siz.