Definition:Basis of Module/Definition 1

Definition

Let $R$ be a ring with unity.

Let $\struct {G, +_G, \circ}_R$ be a unitary $R$-module.

A basis of $G$ is a linearly independent subset of $G$ which is a generator for $G$.

Also see

• Equivalence of Definitions of Basis of Module

Linguistic Note

The plural of basis is bases.

This is properly pronounced bay-seez, not bay-siz.

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 27$. Subspaces and Bases
• 1998: Yoav Peleg, Reuven Pnini and Elyahu Zaarur: Quantum Mechanics ... (previous) ... (next): Chapter $2$: Mathematical Background: $2.2$ Vector Spaces over $C$