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Proceedings of the American Mathematical Society

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

 

 

Congruence relations in direct products


Authors: Grant A. Fraser and Alfred Horn
Journal: Proc. Amer. Math. Soc. 26 (1970), 390-394
MSC: Primary 08.30
DOI: https://doi.org/10.1090/S0002-9939-1970-0265258-1
MathSciNet review: 0265258
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Abstract: This paper studies conditions under which every congruence relation $ \theta $ in a direct product $ A \times B$ of algebras is of the form $ {\theta _1} \times {\theta _2}$, where $ {\theta _1}$ and $ {\theta _2}$ are congruence relations in $ A$ and $ B$ respectively. It is shown that for any equational class $ K$, every such $ \theta $ in every $ A \times B$ in $ K$ has this property if and only if $ K$ satisfies certain identities.


References [Enhancements On Off] (What's this?)

  • [1] G. Grätzer, Universal algebra, University Series in Higher Math., Van Nosstrand, Princeton, N. J., 1968.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0265258-1
Keywords: Congruence relation, direct product, equational class
Article copyright: © Copyright 1970 American Mathematical Society