In a monoid, the notion of inverse as defined in the previous section is strictly narrower than the definition given in this section. Only elements in the Green class "H"1 have an inverse from the unital magma perspective, whereas for any idempotent "e", the elements of "H"e have an inverse as defined in this section. Under this more general definition, inverses need not be unique (or exist) in an arbitrary semigroup or monoid. If all elements are regular, then the semigroup (or monoid) is called regular, and every element has at least one inverse. If every element has exactly one inverse as defined in this section, then the semigroup is called an inverse semigroup. Finally, an inverse semigroup with only one idempotent is a group. An inverse semigroup may have an absorbing element 0 because 000 = 0, whereas a group may not.