A note on strongly -reflexive inverse semigroups

Author:
L. O’Carroll

Journal:
Proc. Amer. Math. Soc. **79** (1980), 352-354

MSC:
Primary 20M10

DOI:
https://doi.org/10.1090/S0002-9939-1980-0567970-X

MathSciNet review:
567970

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Abstract: 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 Green's relation , and in particular if the union is a disjoint one, then *S* is indeed strongly *E*-reflexive. This is established by showing that -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.

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DOI:
https://doi.org/10.1090/S0002-9939-1980-0567970-X

Article copyright:
© Copyright 1980
American Mathematical Society