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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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Some varieties containing relation algebras
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by Roger Maddux PDF
Trans. Amer. Math. Soc. 272 (1982), 501-526 Request permission

Abstract:

Three varieties of algebras are introduced which extend the variety $RA$ of relation algebras. They are obtained from $RA$ by weakening the associative law for relative product, and are consequently called nonassociative, weakly-associative and semiassociative relation algebras, or $NA$, $WA$, and $SA$, respectively. Each of these varieties arises naturally in solving various problems concerning relation algebras. We show, for example, that $WA$ is the only one of these varieties which is closed under the formation of complex algebras of atom structures of algebras, and that $WA$ is the closure of the variety of representable $RA$’s under relativization. The paper also contains a study of the elementary theories of these varieties, various representation theorems, and numerous examples.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 272 (1982), 501-526
  • MSC: Primary 03G15; Secondary 03G25, 06E99, 08C10
  • DOI: https://doi.org/10.1090/S0002-9947-1982-0662049-7
  • MathSciNet review: 662049