On regular semigroups and their multiplication

Author:
Pierre Antoine Grillet

Journal:
Trans. Amer. Math. Soc. **246** (1978), 111-138

MSC:
Primary 20M10

MathSciNet review:
515532

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Abstract: A method is given for the construction of regular semigroups in terms of groups and partially ordered sets. This describes any regular semigroup *S* and its multiplication by means of triples with , and *g* in the Schützenberger group of the corresponding -class. It is shown that the multiplication on *S* is determined by certain simple products. Furthermore the associativity of these simple products implies associativity of the entire multiplication.

**[1]**G. R. Baird,*On semigroups and uniform partial bands*, Semigroup Forum**4**(1972), 185–188. MR**0291321****[2]**A. H. Clifford,*The structure of bisimple left unipotent semigroups as ordered pairs*, Semigroup Forum**5**(1972/73), 137–144. MR**0333040****[3]**A. H. Clifford and G. B. Preston,*The algebraic theory of semigroups. Vol. I*, Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1961. MR**0132791****[4]**Nicolas Farès,*Idempotents et*-*classes dans les demigroups et les anneaux*, C. R. Acad. Sci. Paris Sér. A-B**269**(1969), A341-A343. MR**40**#2777.**[5]**Pierre Antoine Grillet,*Left coset extensions*, Semigroup Forum**7**(1974), no. 1-4, 200–263. Collection of articles dedicated to Alfred Hoblitzelle Clifford on the occasion of his 65th birthday and to Alexander Doniphan Wallace on the occasion of his 68th birthday. MR**0382492****[6]**-,*A coherence theorem for Schützenberger groups*, J. Austral. Math. Soc. (submitted).**[7]**Jonathan Leech,*\cal𝐻-coextensions of monoids*, Mem. Amer. Math. Soc.**1**(1975), no. issue 2, 157, 1–66. MR**0376919**

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DOI:
https://doi.org/10.1090/S0002-9947-1978-0515532-8

Article copyright:
© Copyright 1978
American Mathematical Society