Middle nucleus

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

• Left nucleus
• Right nucleus
• Nucleus