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 $S$.