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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48 .

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One-sided congruences on inverse semigroups
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by John Meakin PDF
Trans. Amer. Math. Soc. 206 (1975), 67-82 Request permission

Abstract:

By the kernel of a one-sided (left or right) congruence $\rho$ on an inverse semigroup $S$, we mean the set of $\rho$-classes which contain idempotents of $S$. We provide a set of independent axioms characterizing the kernel of a one-sided congruence on an inverse semigroup and show how to reconstruct the one-sided congruence from its kernel. Next we show how to characterize those partitions of the idempotents of an inverse semigroup $S$ which are induced by a one-sided congruence on $S$ and provide a characterization of the maximum and minimum one-sided congruences on $S$ inducing a given such partition. The final two sections are devoted to a study of indempotent-separating one-sided congruences and a characterization of all inverse semigroups with only trivial full inverse subsemigroups. A Green-Lagrange-type theorem for finite inverse semigroups is discussed in the fourth section.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 206 (1975), 67-82
  • MSC: Primary 20M10
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0369580-9
  • MathSciNet review: 0369580