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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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Amalgamated products of semigroups: the embedding problem
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by Gérard Lallement PDF
Trans. Amer. Math. Soc. 206 (1975), 375-394 Request permission

Abstract:

A necessary and sufficient condition for a semigroup amalgam to be embeddable is given. It is in the form of a countable set of equational implications with existential quantifiers. Furthermore it is shown that no finite set of equational implications can serve as a necessary and sufficient condition. Howie’s sufficient condition (see [5]) is derived as a consequence of our main theorem.
References
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  • P. A. Grillet and Mario Petrich, Free products of semigroups amalgamating an ideal, J. London Math. Soc. (2) 2 (1970), 389–392. MR 276385, DOI 10.1112/jlms/2.Part_{3}.389
  • T. E. Hall, Inverse semigroups and the amalgamation property (to appear).
  • J. M. Howie, Embedding theorems with amalgamation for semigroups, Proc. London Math. Soc. (3) 12 (1962), 511–534. MR 138696, DOI 10.1112/plms/s3-12.1.511
  • E. S. Ljapin, Intersections of independent subsemigroups of a semigroup, Izv. Vysš. Učebn. Zaved. Matematika 1970 (1970), no. 4 (95), 67–73 (Russian). MR 0281812
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 206 (1975), 375-394
  • MSC: Primary 20M10
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0364505-4
  • MathSciNet review: 0364505