Definition:Subalgebra

Definition

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 $*$.

Also see

• Definition:Unital Subalgebra

• Results about subalgebras can be found here.

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