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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A network of congruences on an inverse semigroup
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by Mario Petrich and Norman R. Reilly PDF
Trans. Amer. Math. Soc. 270 (1982), 309-325 Request permission

Abstract:

A congruence $\rho$ on an inverse semigroup $S$ is determined uniquely by its kernel and its trace. Denoting by ${\rho ^{\min }}$ and ${\rho _{\min }}$ the least congruence on $S$ having the same kernel and the same trace as $\rho$, respectively, and denoting by $\omega$ the universal congruence on $S$, we consider the sequence $\omega$, ${\omega ^{\min }}$, ${\omega _{\min }}$, ${({\omega ^{\min }})_{\min }}$, ${({\omega _{\min }})^{\min }} \ldots$. These congruences, together with the intersections of corresponding pairs, form a sublattice of the lattice of all congruences on $S$. We study the properties of these congruences and establish several properties of the quasivarieties of inverse semigroups induced by them.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 270 (1982), 309-325
  • MSC: Primary 20M10
  • DOI: https://doi.org/10.1090/S0002-9947-1982-0642343-6
  • MathSciNet review: 642343