Original sentence: As defined in this section, inverses need not exist, let alone be unique in an arbitrary semigroup.If all elements are regular, then the semigroup is called regular, and every element has at least one inverse
Edited sentence: An inverse semigroup may have an absorbing element 0 because 000=0, whereas a group may not.If all elements are regular, then the semigroup (or monoid) is called regular, and every element has at least one inverse.Under this more general definition, inverses need not be unique (or exist) in an arbitrary semigroup or monoid