Middle nucleus

From Groupprops
Jump to: navigation, search

Template:Submagma-defining function

Definition

For a magma (S,*), the middle nucleus is the set of elements b \in S such that:

a * (b * c) = (a * b) * c \ \forall \ a,c \in S

The elements of the middle nucleus are termed middle-associative elements or middle nuclear elements.

The middle nucleus of a magma is a submagma that is in fact a semigroup under the induced operation. For full proof, refer: middle-associative elements of magma form submagma

Relation with other submagma-defining functions

Related submagma-defining functions