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Regular semigroups which are subdirect products of a band and a semilattice of groups

Published online by Cambridge University Press:  18 May 2009

Mario Petrich
Mario Petrich
Affiliation:
Pennsylvania State University, University ParkPennsylvania
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In the study of the structure of regular semigroups, it is customary to impose several conditions restricting the behaviour of ideals, idempotents or elements. In a few instances, one may represent them as subdirect products of some much more restricted types of regular semigroups, e.g., completely (0-) simple semigroups, bands, semilattices, etc. In particular, studying the structure of completely regular semigroups, one quickly distinguishes certain special cases of interest when these semigroups are represented as semilattices of completely simple semigroups. In fact, this semilattice of semigroups may be built in a particular way, idempotents may form a subsemigroup, ℋ may be a congruence, and so on.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 14 , Issue 1 , February 1973 , pp. 27 - 49
Copyright
Copyright © Glasgow Mathematical Journal Trust 1973

References

REFERENCES

1.Chrislock, J. L. and Tamura, T., Notes on subdirect products of semigroups and rectangular bands, Proc. Amer. Math. Soc. 20 (1969), 511–514.CrossRefGoogle Scholar
2.Clifford, A. H., Bands of semigroups, Proc. Amer. Math. Soc. 5 (1954), 499–504.CrossRefGoogle Scholar
3.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Amer. Math. Soc, Math. Surveys No. 7, Vol. I (Providence, R.I., 1961).Google Scholar
4.Fantham, P. H. H., On the classification of a certain type of semigroup, Proc. London Math. Soc. 10 (1960), 409–27.CrossRefGoogle Scholar
5.Howie, J. M. and Lallement, G., Certain fundamental congruences on a regular semigroup, Proc. Glasgow Math. Assoc. 7 (1966), 145–156.CrossRefGoogle Scholar
6.Kimura, N., The structure of idempotent semigroups (I), Pacific J. Math. 8 (1958), 257–275.CrossRefGoogle Scholar
7.Petrich, M., Sur certaines classes de demi-groupes I, Acad. Roy. Belg. Bull. Cl. Sci. 49 (1963), 785–798.Google Scholar
8.Petrich, M., The maximal semilattice decomposition of a semigroup, Math. Zeit. 85 (1964), 68–82.CrossRefGoogle Scholar
9.Petrich, M;, The structure of a class of semigroups which are unions of groups, Notices Amer. Math. Soc. 12 (1965), Abstr. No. 619–151.Google Scholar
10.Petrich, M., The maximal matrix decomposition of a semigroup, Portugal. Math. 25 (1966), 15–33.Google Scholar
11.Petrich, M., Regular semigroups satisfying certain conditions on idempotents and ideals, Trans. Amer. Math. Soc. 170 (1972), 245–267.CrossRefGoogle Scholar
12.Yamada, M., Strictly inverse semigroups, Bull. Shimane Univ. 13 (1964), 128–138.Google Scholar
13.Yamada, M., Regular semigroups whose idempotents satisfy permutation identities, Pacific J. Math. 21 (1967), 371–392.CrossRefGoogle Scholar
14.Yamada, M. and Kimura, N., Note on idempotent semigroups II, Proc. Japan Acad. 34 (1958), 110–112.Google Scholar