Definition:Generator of Algebra

This page is about generators of algebras. For other uses, see generator.

Definition

Let $\struct {A_R, \oplus}$ be an algebra over a ring $R$.

Let $S \subseteq A_R$ be a subset of $A_R$.

The subalgebra generated by $S$ is the smallest subalgebra $B_R$ of $A_R$ which contains $S$.

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