Definition:Associative Algebra

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This page is about Associative Algebra. For other uses, see Associative.


Let $R$ be a commutative ring.

Let $\struct {A_R, *}$ be an algebra over $R$.

Then $\struct {A_R, *}$ is an associative algebra if and only if $*$ is an associative operation.

That is:

$\forall a, b, c \in A_R: \paren {a * b} * c = a * \paren {b * c}$

Also see

  • Results about associative algebras can be found here.