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A note on strongly $ E$-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 $ \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 $ \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.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0567970-X
Article copyright: © Copyright 1980 American Mathematical Society

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