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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The potential $\mathcal {J}$-relation and amalgamation bases for finite semigroups
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by T. E. Hall and Mohan S. Putcha PDF
Proc. Amer. Math. Soc. 95 (1985), 361-364 Request permission


Let $S$ be a finite semigroup, $a,b \in S$. When does there exist a finite semigroup $T$ containing $S$ such that $a\mathcal {J}b$ in $T$? This problem was posed to the second named author by John Rhodes in 1974. We show here that if $a$, $b$ are regular, then such a semigroup $T$ exists if and only if either $a\mathcal {J}b$ in $S$, or $a \notin SbS$ and $b \notin SaS$. We use this result to show that analgamation bases for the class of finite semigroups have linearly ordered $\mathcal {J}$-classes.
    A. H. Clifford and G. B. Preston, The algebraic theory of semigroups, Math. Surveys, I and II, Amer. Math. Soc., Providence, R. I., 1961 and 1967.
  • T. E. Hall, On the natural ordering of ${\cal J}$-classes and of idempotents in a regular semigroup, Glasgow Math. J. 11 (1970), 167–168. MR 269761, DOI 10.1017/S0017089500001026
  • T. E. Hall, Free products with amalgamation of inverse semigroups, J. Algebra 34 (1975), 375–385. MR 382518, DOI 10.1016/0021-8693(75)90164-7
  • T. E. Hall, Representation extension and amalgamation for semigroups, Quart. J. Math. Oxford Ser. (2) 29 (1978), no.Β 115, 309–334. MR 509697, DOI 10.1093/qmath/29.3.309
  • β€”, Inverse and regular semigroups and amalgamation: a brief survey, Symposium on Regular Semigroups, De Kalb, Illinois, 1979, pp. 49-79.
  • J. M. Howie, An introduction to semigroup theory, L. M. S. Monographs, No. 7, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1976. MR 0466355
  • John Rhodes, Some results on finite semigroups, J. Algebra 4 (1966), 471–504. MR 201546, DOI 10.1016/0021-8693(66)90035-4
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 95 (1985), 361-364
  • MSC: Primary 20M10
  • DOI:
  • MathSciNet review: 806071