A note on strongly $E$-reflexive inverse semigroups
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- by L. O’Carroll PDF
- Proc. Amer. Math. Soc. 79 (1980), 352-354 Request permission
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.References
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Additional Information
- © Copyright 1980 American Mathematical Society
- 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