Partial groupoid

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 is called a partial semigroup if the following associative law holds:

For all such that and , the following two statements hold:

1. if and only if , and
2. if (and, because of 1., also ).

References

Further reading