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.

Related submagma-defining functions

 * Left nucleus is the right nucleus for the opposite binary operation.
 * Middle nucleus
 * Nucleus