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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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Certain dense embeddings of regular semigroups
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by Mario Petrich PDF
Trans. Amer. Math. Soc. 155 (1971), 333-343 Request permission

Abstract:

In a previous paper, the author has introduced a number of homomorphisms of an arbitrary semigroup into the translational hull of certain Rees matrix semigroups or orthogonal sums thereof. For regular semigroups, it is proved here that all of these homomorphisms have the property that the image is a densely embedded subsemigroup, i.e., is a densely embedded ideal of its idealizer, and that the corresponding Rees matrix semigroups are regular. Several of these homomorphisms are 1-1, in each case they furnish a different dense embedding of an arbitrary regular semigroup into the translational hull of a regular Rees matrix semigroup or orthogonal sums thereof. A new representation for regular semigroups is introduced.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 155 (1971), 333-343
  • MSC: Primary 20.92
  • DOI: https://doi.org/10.1090/S0002-9947-1971-0276383-9
  • MathSciNet review: 0276383