Category:Definitions/Bases of Vector Spaces

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This category contains definitions related to Bases of Vector Spaces.
Related results can be found in Category:Bases of Vector Spaces.

Let $K$ be a division ring.

Let $\struct {G, +_G, \circ}_R$ be a vector space over $K$.

Definition 1

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

Definition 2

A basis is a maximal linearly independent subset of $G$.