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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Finite simple abelian algebras are strictly simple
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by Matthew A. Valeriote PDF
Proc. Amer. Math. Soc. 108 (1990), 49-57 Request permission

Abstract:

A finite universal algebra is called strictly simple if it is simple and has no nontrivial subalgebras. An algebra is said to be Abelian if for every term $t(x,\bar y)$ and for all elements $a,b,\bar c,\bar d$, we have the following implication: $t(a,\bar c) = t(a,\bar d) \to t(b,\bar c) = t(b,\bar d)$. It is shown that every finite simple Abelian universal algebra is strictly simple. This generalizes a well-known fact about Abelian groups and modules.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 108 (1990), 49-57
  • MSC: Primary 08A30; Secondary 03C05
  • DOI: https://doi.org/10.1090/S0002-9939-1990-0990434-2
  • MathSciNet review: 990434