Hostname: page-component-848d4c4894-nmvwc Total loading time: 0 Render date: 2024-06-20T17:31:34.633Z Has data issue: false hasContentIssue false
  • English
  • Français

Congruence-free regular semigroups

Published online by Cambridge University Press:  20 January 2009

W. D. Munn
W. D. Munn
Affiliation:
Department of MathematicsUniversity of GlasgowGlasgow G12 8QW, Scotland
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A semigroup is said to be congruence-free if and only if its only congruences are the universal relation and the identical relation. Congruence-free inverse semigroups were studied by Baird [2], Trotter [19], Munn [15,16] and Reilly [18]. In addition, results on congruence-free regular semigroups have been obtained by Trotter [20], Hall [4] and Howie [7].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 28 , Issue 1 , February 1985 , pp. 113 - 119
Copyright
Copyright © Edinburgh Mathematical Society 1985

References

REFERENCES

1.Bailes, G. L. Jr., Right inverse semigroups, J. Algebra 26 (1973), 492–507.CrossRefGoogle Scholar
2.Baird, G. R., Congruence-free inverse semigroups with zero, J. Austral. Math. Soc. (A) 20 (1975), 110–114.CrossRefGoogle Scholar
3.Hall, T. E., On regular semigroups, J. Algebra 24 (1973), 1–24.CrossRefGoogle Scholar
4.Hall, T. E., Amalgamation and inverse and regular semigroups: a brief survey, Proc. conference on regular semigroups (Northern Illinois University, 1979).Google Scholar
5.Hall, T. E. and Munn, W. D., The hypercore of a semigroup, Proc. Edinburgh Math. Soc. 28 (1985), 107–112.CrossRefGoogle Scholar
6.Howie, J. M., An introduction to semigroup theory (Academic Press, New York, 1976).Google Scholar
7.Howie, J. M., A class of bisimple, idempotent-generated congruence-free semigroups, Proc. Roy. Soc. Edinburgh (A) 88 (1981), 169–184.CrossRefGoogle Scholar
8.Feigenbaum, R., Kernels of regular semigroup homomorphisms (Ph.D. dissertation, University of South Carolina, 1975).Google Scholar
9.Feigenbaum, R., Regular semigroup congruences, Semigroup Forum 17 (1979), 373–377.CrossRefGoogle Scholar
10.Lallement, G., Congruences et équivalences de Green sur un demi-groupe régulier, C.R. Acad. Sci. Paris Sér. A 262 (1966), 613–616.Google Scholar
11.McAlister, D. B., Regular semigroups, fundamental semigroups and groups, J. Austral. Math. Soc. (A) 29 (1980), 475–503.CrossRefGoogle Scholar
12.Munn, W. D., A class of irreducible matrix representations of an arbitrary inverse semigroup, Proc. Glasgow Math. Assoc. 5 (1961), 41–48.CrossRefGoogle Scholar
13.Munn, W. D., Uniform semilattices and bisimple inverse semigroups, Quart. J. Math. (Oxford) (2) 17 (1966), 151–159.CrossRefGoogle Scholar
14.Munn, W. D., Fundamental inverse semigroups, Quart. J. Math. (Oxford) (2) 21 (1970), 157–170.CrossRefGoogle Scholar
15.Munn, W. D., Congruence-free inverse semigroups, Quart. J. Math. (Oxford) (2) 25 (1974), 463–484.CrossRefGoogle Scholar
16.Munn, W. D., A note on congruence-free inverse semigroups, Quart. J. Math. (Oxford) (2) 26 (1975), 385–387.CrossRefGoogle Scholar
17.Nambooripad, K. S. S., Structure of regular semigroups I, Mem. Amer. Math. Soc. 224 (1979).Google Scholar
18.Reilly, N. R., Congruence-free semigroups, Proc. London Math. Soc. (3) 33 (1976), 497–514.CrossRefGoogle Scholar
19.Trotter, P. G., Congruence-free inverse semigroups, Semigroup Forum 9 (1974), 109–116.CrossRefGoogle Scholar
20.Trotter, P. G., Congruence-free regular semigroups with zero, Semigroup Forum 12 (1976), 1–5.CrossRefGoogle Scholar