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

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

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
\Bibitem{San03} \by N.~I.~Sandu \paper Infinite Independent Systems of Identities of an Associative Algebra over an Infinite Field of Characteristic Two \jour Mat. Zametki \yr 2003 \vol 74 \issue 4 \pages 603--611 \mathnet{http://mi.mathnet.ru/mz292} \crossref{https://doi.org/10.4213/mzm292} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2042973} \zmath{https://zbmath.org/?q=an:1068.16024} \transl \jour Math. Notes \yr 2003 \vol 74 \issue 4 \pages 569--577 \crossref{https://doi.org/10.1023/A:1026156113443} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000186455400031} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0347125007} 

• http://mi.mathnet.ru/eng/mz292
• https://doi.org/10.4213/mzm292
• http://mi.mathnet.ru/eng/mz/v74/i4/p603

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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
2. Balla K., Linh Vu Hoang, “Adjoint pairs of differential-algebraic equations and Hamiltonian systems”, Appl. Numer. Math., 53:2–4 (2005), 131–148
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