Category:Definitions/Vector Spaces

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


Let $\struct {K, +_K, \times_K}$ be a division ring.

Let $\struct {G, +_G}$ be an abelian group.

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


Then $\struct {G, +_G, \circ}_K$ is a vector space over $K$ or a $K$-vector space.


That is, a vector space is a unitary module whose scalar ring is a division ring.

Subcategories

This category has the following 8 subcategories, out of 8 total.