[[K-monoid|$\mathbb K$-ring]]
# $\mathbb{K}$-subring

A **$\mathbb{K}$-subring** $B$ of an [[K-monoid|$\mathbb K$-ring]] $A$ is a [[Subalgebra over a field|subalgebra]] $B \leq A$ containing the identity, #m/def/falg 
i.e. $B$ is itself an associative algebra; $B \cdot B \sube B$ and $\mathbb{1} \in B$.

## Properties

- The [[commutator]] algebra of an associative subalgebra is a [[Lie subalgebra]]

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#state/develop | #lang/en | #SemBr