Left nucleus

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Template:Submagma-defining function

Definition

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

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

Elements of the left nucleus are termed left-associative elements or left nuclear elements.

The left nucleus of a magma is a submagma. In fact, it is a subsemigroup that contains any left neutral element of the magma and also any left nil of the magma. For full proof, refer: left-associative elements of magma form submagma