Proper regular semigroups
HTML articles powered by AMS MathViewer
- by F. E. Masat PDF
- Proc. Amer. Math. Soc. 71 (1978), 189-192 Request permission
Abstract:
In a recent paper, D. B. McAlister gave several characterizations of proper inverse semigroups. In this paper, the concept of proper is extended to the class of regular semigroups. This is done by requiring that the set of idempotents of the semigroup coincides with the kernel of the minimum group congruence on the semigroup. A theorem is presented which contains several characterizations of proper regular semigroups, and the related result of McAlister then follows as a corollary. The paper concludes with some open questions and examples.References
- A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. Vol. I, Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1961. MR 0132791 —, The algebraic theory of semigroups. II, Math. Surveys, no. 7, Amer. Math. Soc., Providence, R. I., 1967; reprinted with corrections, 1971.
- T. E. Hall, On regular semigroups whose idempotents form a subsemigroup, Bull. Austral. Math. Soc. 1 (1969), 195–208. MR 249527, DOI 10.1017/S0004972700041447
- J. M. Howie, An introduction to semigroup theory, L. M. S. Monographs, No. 7, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1976. MR 0466355
- J. M. Howie and G. Lallement, Certain fundamental congruences on a regular semigroup, Proc. Glasgow Math. Assoc. 7 (1966), 145–159. MR 197598
- Francis E. Masat, Right group and group congruences on a regular semigroup, Duke Math. J. 40 (1973), 393–402. MR 318378
- D. B. McAlister, Groups, semilattices and inverse semigroups. I, II, Trans. Amer. Math. Soc. 192 (1974), 227–244; ibid. 196 (1974), 351–370. MR 357660, DOI 10.1090/S0002-9947-1974-0357660-2
- R. R. Stoll, Homomorphisms of a semigroup onto a group, Amer. J. Math. 73 (1951), 475–481. MR 41128, DOI 10.2307/2372188
- Tôru Saitô, Proper ordered inverse semigroups, Pacific J. Math. 15 (1965), 649–666. MR 191977
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 71 (1978), 189-192
- MSC: Primary 20M10
- DOI: https://doi.org/10.1090/S0002-9939-1978-0480796-1
- MathSciNet review: 0480796