Partial groupoid - Alchetron, The Free Social Encyclopedia

In abstract algebra, a partial groupoid (also called halfgroupoid, pargoid, or partial magma) is a set endowed with a partial binary operation.

A partial groupoid is a partial algebra.

Partial semigroup

A partial groupoid ( M , ∘ ) is called a partial semigroup if the following associative law holds:

Let x , y , z ∈ G such that x ∘ y ∈ G and y ∘ z ∈ G , then

x ∘ ( y ∘ z ) ∈ G if and only if ( x ∘ y ) ∘ z ∈ G
and x ∘ ( y ∘ z ) = ( x ∘ y ) ∘ z if x ∘ ( y ∘ z ) ∈ G (and, because of 1., also ( x ∘ y ) ∘ z ∈ G ).

References

Partial groupoid Wikipedia

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