Completely semisimple semigroups and epimorphisms
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- by Peter M. Higgins PDF
- Proc. Amer. Math. Soc. 96 (1986), 387-390 Request permission
Abstract:
It is proved that a completely semisimple semigroup $U$ cannot be properly epimorphically embedded in another semigroup if $U$ has no infinite chain of $\mathcal {J}$-classes.References
- T. E. Hall, Epimorphisms and dominions, Semigroup Forum 24 (1982), no. 2-3, 271–283. MR 650576, DOI 10.1007/BF02572773
- T. E. Hall and P. R. Jones, Epis are onto for finite regular semigroups, Proc. Edinburgh Math. Soc. (2) 26 (1983), no. 2, 151–162. MR 705258, DOI 10.1017/S0013091500016850
- P. M. Higgins, Epis are onto for generalised inverse semigroups, Semigroup Forum 23 (1981), no. 3, 255–259. MR 647117, DOI 10.1007/BF02676649 —, The commutative varieties of semigroups for which epis are onto, Proc. Edinburgh Math. Soc. 94A (1983), 1-7.
- Peter M. Higgins, A semigroup with an epimorphically embedded subband, Bull. Austral. Math. Soc. 27 (1983), no. 2, 231–242. MR 707973, DOI 10.1017/S0004972700025715
- Peter M. Higgins, Epimorphisms, permutation identities and finite semigroups, Semigroup Forum 29 (1984), no. 1-2, 87–97. MR 742126, DOI 10.1007/BF02573318
- 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
- John R. Isbell, Epimorphisms and dominions, Proc. Conf. Categorical Algebra (La Jolla, Calif., 1965) Springer, New York, 1966, pp. 232–246. MR 0209202
- John R. Isbell, Epimorphisms and dominions, Proc. Conf. Categorical Algebra (La Jolla, Calif., 1965) Springer, New York, 1966, pp. 232–246. MR 0209202
- H. E. Scheiblich and Kayran C. Moore, $T_{X}$ is absolutely closed, Semigroup Forum 6 (1973), no. 3, 216–226. MR 374316, DOI 10.1007/BF02389124
- Kunitaka Shoji, Injective hulls of certain right reductive semigroups as right $S$-systems, Mem. Fac. Sci. Shimane Univ. 14 (1980), 25–34. MR 608369
- P. G. Trotter, A nonsurjective epimorphism of bands, Algebra Universalis 22 (1986), no. 2-3, 109–116. MR 870459, DOI 10.1007/BF01224017
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 387-390
- MSC: Primary 20M50
- DOI: https://doi.org/10.1090/S0002-9939-1986-0822424-3
- MathSciNet review: 822424