Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-25T23:25:09.270Z Has data issue: false hasContentIssue false

Congruences and Green's relations on regular semigroups

Published online by Cambridge University Press:  18 May 2009

T. E. Hall
Affiliation:
University of Stirling
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.

It is sometimes possible to reconstruct semigroups from some of their homomorphic images. Some recent examples have been the construction of bisimple inverse semigroups from fundamental bisimple inverse semigroups [9], and the construction of generalized inverse semigroups from inverse semigroups [12].

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1972

References

REFERENCES

1.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Amer. Math. Soc., Mathematical Surveys No. 7, Vols. I and II (Providence, R. I., 1961 and 1967).Google Scholar
2.Hall, T. E., On the lattice of congruences on a regular semigroup, Bull. Australian Math. Soc. 1 (1969), 231235.CrossRefGoogle Scholar
3.Hall, T. E., On regular semigroups, J. Algebra; to appear.Google Scholar
4.Howie, J. M. and Lallement, G., Certain fundamental congruences on a regular semigroup, Proc. Glasgow Math. Assoc. 7 (1966), 145159.CrossRefGoogle Scholar
5.Rhodes, J., Some results on finite semigroups, J. Algebra 4 (1966), 471504.CrossRefGoogle Scholar
6.Lallement, G., Congruences et équivalences de Green sur un demi-groupe régulier, C. R. Acad. Sc. Paris, Série A, 262 (1966), 613616.Google Scholar
7.Munn, W. D., Regular w-semigroups, Glasgow Math. J. 9 (1968), 4666.CrossRefGoogle Scholar
8.Munn, W. D., On simple inverse semigroups, Semigroup Forum 1 (1970), 6374.CrossRefGoogle Scholar
9.Munn, W. D., 0-bisimple inverse semigroups, J. Algebra 15 (1970), 570588.CrossRefGoogle Scholar
10.Preston, G. B., Matrix representations of inverse semigroups, J. Australian Math. Soc. 9 (1969), 2961.CrossRefGoogle Scholar
11.Reilly, N. R. and Scheiblich, H. E., Congruences on regular semigroups, Pacific J. Math. 23 (1967), 349360.CrossRefGoogle Scholar
12.Yamada, M., Regular semigroups whose idempotents satisfy permutation identities, Pacific J. Math. 21 (1967), 371392.CrossRefGoogle Scholar