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This article is cited in 4 scientific papers (total in 4 papers)
On Some Extremal Varieties of Associative Algebras
E. A. Kireevaa, A. N. Krasilnikovb
a Moscow State Pedagogical University
b University of Brasilia
Abstract:
Suppose that $F$ is a field of prime characteristic $p$ and $\mathbf V_p$ is the variety of associative algebras over $F$ defined by the identities $[[x,y],z]=0$ and $x^p=0$ if $p>2$ and by the identities $[[x,y],z]=0$ and $x^4=0$ if $p=2$ (here $[x,y]=xy-yx$). As is known, the free algebras of countable rank of the varieties $\mathbf V_p$ contain non-finitely generated $T$-spaces. We prove that the varieties $\mathbf V_p$ are minimal with respect to this property.
DOI:
https://doi.org/10.4213/mzm2613
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English version:
Mathematical Notes, 2005, 78:4, 503–517
Bibliographic databases:
    
UDC:
512.552
Received: 15.10.2004
Citation:
E. A. Kireeva, A. N. Krasilnikov, “On Some Extremal Varieties of Associative Algebras”, Mat. Zametki, 78:4 (2005), 542–558; Math. Notes, 78:4 (2005), 503–517
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/mz2613https://doi.org/10.4213/mzm2613 http://mi.mathnet.ru/eng/mz/v78/i4/p542
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This publication is cited in the following articles:
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A. V. Grishin, “Structural and algorithmic problems in $T$-spaces over a field of characteristic $p>0$”, Russian Math. Surveys, 60:3 (2005), 568–569
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E. A. Kireeva, “Limit T-spaces”, J. Math. Sci., 152:4 (2008), 540–557
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A. V. Grishin, L. M. Tsybulya, “On the structure of a relatively free Grassmann algebra”, J. Math. Sci., 171:2 (2010), 149–212
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Brandão Antônio Pereira J., Koshlukov P., Krasilnikov A., da Silva É.A., “The central polynomials for the Grassmann algebra”, Israel J. Math., 179:1 (2010), 127–144
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