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Transactions of the American Mathematical Society

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

 
 

 

One-sided congruences on inverse semigroups


Author: John Meakin
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
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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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DOI: https://doi.org/10.1090/S0002-9947-1975-0369580-9
Article copyright: © Copyright 1975 American Mathematical Society

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