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Mat. Zametki, 2003, Volume 74, Issue 4, Pages 603–611 (Mi mz292)  

This article is cited in 2 scientific papers (total in 2 papers)

Infinite Independent Systems of Identities of an Associative Algebra over an Infinite Field of Characteristic Two

N. I. Sandu

State Agricultural University of Moldova

Abstract: Let $\mathfrak B$ be the variety of associative (special Jordan, respectively) algebras over an infinite field of characteristic 2 defined by the identity $((((x_1,x_2),x_3),((x_4,x_5),x_6)),(x_7,x_8))=0$ ($((x_1x_2\cdot x_3)(x_4x_5\cdot x_6))(x_7x_8)=0$, respectively). In this paper, we construct infinite independent systems of identities in the variety $\mathfrak B$ ($\mathfrak D$ , respectively). This implies that the set of distinct nonfinitely based subvarieties of the variety $\mathfrak B$ has the cardinality of the continuum and that there are algebras in $\mathfrak B$ with undecidable word problem.

DOI: https://doi.org/10.4213/mzm292

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English version:
Mathematical Notes, 2003, 74:4, 569–577

Bibliographic databases:

UDC: 519.48
Received: 29.03.1999

Citation: N. I. Sandu, “Infinite Independent Systems of Identities of an Associative Algebra over an Infinite Field of Characteristic Two”, Mat. Zametki, 74:4 (2003), 603–611; Math. Notes, 74:4 (2003), 569–577

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. Sandu N. I., “Infinite independent systems of the identities of the associative algebra over an infinite field of characteristic $p>0$”, Czechoslovak Math. J., 55:1 (2005), 1–23  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Balla K., Linh Vu Hoang, “Adjoint pairs of differential-algebraic equations and Hamiltonian systems”, Appl. Numer. Math., 53:2–4 (2005), 131–148  crossref  mathscinet  zmath  isi  elib  scopus  scopus
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