Category:Bases of Modules

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This category contains results about Bases of Modules.
Definitions specific to this category can be found in Definitions/Bases of Modules.

Let $R$ be a ring with unity.

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


Definition 1

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


Definition 2

Let $\BB = \family {b_i}_{i \mathop \in I}$ be a family of elements of $M$.

Let $\Psi: R^{\paren I} \to M$ be the homomorphism given by Universal Property of Free Module on Set.


Then $\BB$ is a basis of $G$ if and only if $\Psi$ is an isomorphism.

Subcategories

This category has only the following subcategory.

C