Nucleus of a magma

From Groupprops
(Redirected from Associative center)

Definition

The nucleus, associative center or associative kernel of a magma is defined as the subset comprising those elements that are left-associative, middle-associative, and right-associative.

The term nucleus is typically used when the magma is an algebra loop.

Particular cases

Additional condition on binary operation Name for magma with that additional condition What can we say about the nucleus?
commutative binary operation commutative magma same as the left nucleus, middle nucleus, or right nucleus
associative binary operation semigroup equal to the whole semigroup