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This article is cited in 8 scientific papers (total in 8 papers)
No associative $PI$-algebra coincides with its commutant
A. Ya. Belovab
a Moscow Institute of Open Education
b International University Bremen
Abstract:
We prove that each (possibly not finitely generated) associative $PI$-algebra does not coincide with its commutant. We thus solve I. V. L'vov's problem in the Dniester Notebook. The result follows from the fact (also established in this article) that, in every $T$-prime variety, some weak identity holds and there exists a central polynomial (the existence of a central polynomial was earlier proved by A. R. Kemer). Moreover, we prove stability of $T$-prime varieties (in the case of characteristic zero, this was done by S. V. Okhitin who used A. R. Kemer's classification of $T$-prime varieties).
Keywords:
PI-algebra, variety of algebras, identity, stable variety, weak identity, identity with trace, forms, Capelli identity, T-prime variety, Hamilton?Cayley equation, central polynomial
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English version:
Siberian Mathematical Journal, 2003, 44:6, 969–980
Bibliographic databases:
   
UDC:
512.552.4, 512.554.32, 512.664.2
Received: 12.05.2003
Citation:
A. Ya. Belov, “No associative $PI$-algebra coincides with its commutant”, Sibirsk. Mat. Zh., 44:6 (2003), 1239–1254; Siberian Math. J., 44:6 (2003), 969–980
Citation in format AMSBIB
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\jour Siberian Math. J.
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http://mi.mathnet.ru/eng/smj1251 http://mi.mathnet.ru/eng/smj/v44/i6/p1239
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A. R. Chekhlov, Ml. V. Agafontseva, “Ob abelevykh gruppakh s tsentralnymi kvadratami kommutatorov endomorfizmov”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2013, no. 4(24), 54–59
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Pereira da Silva e Silva D.D., “a Primeness Property For Central Polynomials of Verbally Prime Pi Algebras”, Linear Multilinear Algebra, 63:11 (2015), 2151–2158
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L. M. Samoilov, “On the Primality Property of Central Polynomials of Prime Varieties of Associative Algebras”, Math. Notes, 99:3 (2016), 413–416
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