Category:Vector Subspaces

This category contains results about Vector Subspaces.
Definitions specific to this category can be found in Definitions/Vector Subspaces.

Let $K$ be a division ring.

Let $\struct {S, +, \circ}_K$ be a $K$-algebraic structure with one operation.

Let $T$ be a closed subset of $S$.

Let $\struct {T, +_T, \circ_T}_K$ be a $K$-vector space where:

$+_T$ is the restriction of $+$ to $T \times T$ and

$\circ_T$ is the restriction of $\circ$ to $K \times T$.

Then $\struct {T, +_T, \circ_T}_K$ is a (vector) subspace of $\struct {S, +, \circ}_K$.