Category:Definitions/Power-Associative Algebras

This category contains definitions related to Power-Associative Algebras.
Related results can be found in Category:Power-Associative Algebras.

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

Then $\struct {A_R, \oplus}$ is a power-associative algebra if and only if $\oplus$ is power-associative.

That is:

For all $a \in A_R$, the subalgebra generated by $\set a$ is an associative algebra.