Category:Subalgebras

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

Let $R$ be a commutative ring.

Let $\struct {A, *}$ be an algebra over $R$.

A subalgebra of $A$ is a submodule $B \subseteq A$ such that:

$\forall x, y \in B: x * y \in B$

That is, such that $B$ is closed under $*$.