Hostname: page-component-cb9f654ff-mnl9s Total loading time: 0 Render date: 2025-08-27T04:33:25.637Z Has data issue: false hasContentIssue false
  • English
  • Français

Extensions of I-Bisimple Semigroups

Published online by Cambridge University Press:  20 November 2018

R. J. Warne
R. J. Warne*
Affiliation:
West Virginia University, Morgantown, West Virginia
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 bisimple semigroup S is called I-bisimple if Es, the set of idempotents of S, with its natural order is order-isomorphic to I, the set of integers, under the reverse of the usual order. In (9), the author completely determined the structure of I-bisimple semigroups mod groups; in this paper, he also gave an isomorphism theorem, a homomorphism theorem, an explicit determination of the maximal group homomorphic image, and a complete determination of the congruences for these semigroups.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 419 - 426
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Clifford, A. H., Extensions of semigroups, Trans. Amer. Math. Soc., 68 (1950), 165–173.Google Scholar
2. Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, vol. 1, Math. Surveys, No. 7, Amer. Math. Soc. (Providence, 1961).Google Scholar
3. Warne, R. J., A characterization of certain regular d-classes in semi-groups, Illinois J. Math., 9 (1965), 304–306.Google Scholar
4. Warne, R. J., Regular d-classes whose idempotents obey certain conditions, Duke Math. J., 33 (1966), 187–196.Google Scholar
5. Warne, R. J., Extensions of completely 0-simple semigroups by completely 0-simple semigroups, Proc. Amer. Math. Soc., to appear.Google Scholar
6. Warne, R. J., A class of bisimple inverse semigroups, Pacific J. Math., to appear.Google Scholar
7. Warne, R. J., Extensions of Brandt semigroups, to appear.Google Scholar
8. Warne, R. J., I-bisimple semigroups, to appear.Google Scholar