Nucleus of a magma
(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 |