Geodesic
Bisimple Inverse Semigroups as Semigroups of Ordered Triples
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 25-39

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In (8) and (13) it has been shown that certain bisimple inverse semigroups, called bisimple ω-semigroups and bisimple Z-semigroups, can be represented as semigroups of ordered triples. In these cases, two of the components of each triple are integers, and the third is drawn from a fixed group. This representation is analogous to that given by the theorem of Rees (1, p. 94) concerning completely simple semigroups, and shares the same advantages. 
Reilly, N. R.; Clifford, A. H. Bisimple Inverse Semigroups as Semigroups of Ordered Triples. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 25-39. doi: 10.4153/CJM-1968-004-4
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[1] 1. Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Math. Surveys No. 7 (American Mathematical Society, Providence, R.I., 1961). Google Scholar

[2] 2. Howie, J. M., The maximum idempotent-separating congruence on an inverse semigroup, Proc. Edinburgh Math. Soc. (II), 20 (1964), 71–79. Google Scholar

[3] 3. Kurosh, A. G., The theory of groups, translated by Hirsch, K. A. (New York, 1956). Google Scholar

[4] 4. Preston, G. B., Inverse semi-groups, J. London Math. Soc, 29 (1954), 396–403. Google Scholar

[5] 5. Preston, G. B., Congruences on completely C-simple semigroups, Proc. London Math. Soc. (3), 11 1961), 557–576. Google Scholar

[6] 6. Rédei, L., Die Verallgemeinerung der Schreierschen Erweiterungstheorie, Acta Sci. Math. Szeged, 15 (1952), 252–273. Google Scholar

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

[8] 8. Reilly, N. R., Bisimple ω-semigroups, Proc. Glasgow Math. Assoc, 7 (1966), 160–167. Google Scholar

[9] 9. Reilly, N. R., Bisimple inverse semigroups, to appear. Google Scholar

[10] 10. Warne, R. J., Homomorphisms of d-simple inverse semigroups with identity, Pacific J. Math., 22 (1964), 1111–1122. Google Scholar

[11] 11. Warne, R. J., Regular d-classes whose idempotents obey certain conditions, Duke J. Math., 33 (1966), 187–195. Google Scholar

[12] 12. Warne, R. J., The idempotent separating congruences of a bisimple inverse semigroup with identity, to appear. Google Scholar

[13] 13. Warne, R. J., Bisimple Z-semigroups, to appear. Google Scholar

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