Right nucleus

Definition

For a magma $(S,*)$ , the right nucleus is the set of $c\in S$ such that:

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

Elements in the right nucleus are termed right-associative elements or right nuclear elements.

The right nucleus of a magma is a submagma, and is a semigroup under the induced operation. For full proof, refer: right-associative elements of magma form submagma