Bisimple ω-Semigroups
Glasgow mathematical journal, Tome 7 (1966) no. 3, pp. 160-167

Voir la notice de l'article provenant de la source Cambridge University Press

The structure of a bisimple inverse semigroup with an identity has been related by Clifford [2] to that of its right unit subsemigroup. In this paper we give an explicit structure theorem for bisimple inverse semigroups in which the idempotents form a simple descending chaine0 > e1 > e2....We call such a semigroup a bisimple co-semigroup. The structure of a semigroup of this kind is shown to be determined entirely by its group of units and an endomorphism of its group of units.
Reilly, N. R. Bisimple ω-Semigroups. Glasgow mathematical journal, Tome 7 (1966) no. 3, pp. 160-167. doi: 10.1017/S2040618500035346
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[1] 1.Bruck, R. H., A survey of binary systems, Ergebnisse der Math., Neue Folge, Vol. 20 (Berlin, 1958). Google Scholar | DOI

[2] 2.Clifford, A. H., A class of d-simple semigroups, Amer. J. Math. 75 (1953), 547–556. Google Scholar | DOI

[3] 3.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, American Mathematical Society Mathematical Surveys No. 7, Vol. 1 (Providence, R. I., 1961). Google Scholar

[4] 4.Munn, W. D. and Reilly, N. R., Congruences on a bisimple ω-semigroup, Proc. Glasgow Math. Assoc. (to appear). Google Scholar

[5] 5.Rees, D., On semigroups, Proc. Cambridge Philos. Soc. 36 (1940), 387–400. Google Scholar | DOI

[6] 6.Rees, D., On the ideal structure of a semigroup satisfying a cancellation law, Quart. J. Math. Oxford Ser. (2) 19 (1948), 101–108. Google Scholar | DOI

[7] 7.Warne, R. J., Homomorphisms of d-simple inverse semigroups with identity, Pacific J. Math. 14 (1964), 1111–1122. Google Scholar | DOI

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