A note on strongly šø-reflexive inverse semigroups
Liam OāCarroll Ā· Proceedings of the American Mathematical Society Ā· 1980
In contrast to the semilattice of groups case, an inverse semigroup S which is the union of strongly E -reflexive inverse subsemigroups need not be strongly E -reflexive. If, however, the union is saturated with respect to the Greenās relation D \mathcal {D} , and in particular if the union is a disjoint one, then S is indeed strongly E -reflexive. This is established by showing that D \mathcal {D} -saturated inverse subsemigroups have certain pleasant properties. Finally, in contrast to the E -unitary case, it is shown that the class of strongly E -reflexive inverse semigroups is not closed under free inverse products.