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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
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.

References [Enhancements On Off] (What's this?)

  • [1] A. H. Clifford and G. B. Preston, The algebraic theory of semigroups, vols. 1, 2, Math. Surveys No. 7, Amer. Math. Soc., Providence, R. I., 1961 and 1967.
  • [2] J. M. Howie, An introduction to semigroup theory, Academic Press, London, 1976. MR 0466355 (57:6235)
  • [3] D. B. McAlister, Inverse semigroups generated by a pair of subgroups, Proc. Roy. Soc. Edinburgh Sect. A. 77 (1977), 9-22. MR 0450438 (56:8732)
  • [4] L. O'Carroll, Strongly E-reflexive inverse semigroups, Proc. Edinburgh Math. Soc. 20 (1976-77), 339-354. MR 0453899 (56:12152)
  • [5] -, Strongly E-reflexive inverse semigroups. II, Proc. Edinburgh Math. Soc. 21 (1978), 1-10. MR 0480799 (58:949)

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