Right group congruences on a semigroup
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- by Francis E. Masat PDF
- Proc. Amer. Math. Soc. 50 (1975), 107-114 Request permission
Abstract:
This paper develops necessary and sufficient conditions on an algebraic semigroup $S$ in order that it will have nontrivial right group homomorphic images. A central notion used is that of how the normal subsemigroups associated with the group images of $S$ relate to the right group images of $S$. The results presented thus extend those of R. R. Stoll. Where right group congruences exist, the structure of $S$ is determined and the right group congruences are characterized in terms of group congruences and right zero congruences on $S$. Sufficient conditions are then found for the existence of a minimum right group congruence on $S$, and isomorphic right group congruences and the minimum right group congruence on $S$ are described. Lastly, an application is made to regular semigroups whose idempotents form a rectangular band.References
- A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. Vol. II, Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1967. MR 0218472 —, The algebraic theory of semigroups. Vol. II, Math. Surveys, no. 7, Amer. Math. Soc., Providence, R.I., 1961. MR 36 #1558.
- 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
- R. R. Stoll, Homomorphisms of a semigroup onto a group, Amer. J. Math. 73 (1951), 475–481. MR 41128, DOI 10.2307/2372188
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 50 (1975), 107-114
- MSC: Primary 20M10
- DOI: https://doi.org/10.1090/S0002-9939-1975-0372085-8
- MathSciNet review: 0372085