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Proceedings of the American Mathematical Society

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

 

 

Definable principal congruences and $ R$-stable identities


Author: G. E. Simons
Journal: Proc. Amer. Math. Soc. 97 (1986), 11-15
MSC: Primary 16A70; Secondary 08B99, 16A38
DOI: https://doi.org/10.1090/S0002-9939-1986-0831376-1
MathSciNet review: 831376
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Abstract: We show that an algebra over an infinite field generates a variety with definable principal congruences if and only if it is commutative. A similar result is proved for polynomial rings. The main tool used is the notion from the theory of PI-rings of an $ R$-stable identity.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0831376-1
Keywords: Varieties of rings, definable principal congruences, stable identities
Article copyright: © Copyright 1986 American Mathematical Society