Original sentence: By contrast, zero has no multiplicative inverse
Edited sentence: All examples in this section involve associative operators, thus we shall use the terms left/right inverse for the unital magma-based definition, and quasi-inverse for its more general version.By contrast, zero has no multiplicative inverse, but it has a unique quasi-inverse, 0 itself.LGL = L and GLG = G and one uniquely determines the other.Only bijections have two-sided inverses, but any function has a quasi-inverse, i.The lower and upper adjoints in a (monotone) Galois connection, L and G are quasi-inverses of each other, i.The monoid of partial functions is also regular, whereas the monoid of injective partial transformations is the prototypical inverse semigroup.They are not left or right inverses of each other however.the full transformation monoid is regular