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Mat. Zametki, 2005, Volume 78, Issue 4, Pages 542–558 (Mi mz2613)  

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    2. E. A. Kireeva, “Limit T-spaces”, J. Math. Sci., 152:4 (2008), 540–557  mathnet  crossref  mathscinet  zmath
    3. A. V. Grishin, L. M. Tsybulya, “On the structure of a relatively free Grassmann algebra”, J. Math. Sci., 171:2 (2010), 149–212  mathnet  crossref  mathscinet  elib
    4. 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  crossref  mathscinet  zmath  isi  elib  scopus  scopus
  • Математические заметки Mathematical Notes
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