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Matematicheskie Trudy, 2000, Volume 3, Number 2, Pages 146–170 (Mi mt170)  

This article is cited in 1 scientific paper (total in 1 paper)

On Some Algorithmic Problems Related to Varieties of Nonassociative Rings

V. Yu. Popov

Ural State Technical University
Full-text PDF (354 kB) Citations (1)
Abstract: It is proven that there exists no algorithm deciding whether the variety $\mathrm{var}\Sigma$ is finitely based relative to an arbitrary recursive system of ring identities $\Sigma$. An infinite sequence is constructed of finitely based varieties of nonassociative rings $\mathfrak A_1\supset\mathfrak B_1\supset\mathfrak A_2\supset\mathfrak B_2 \supset\dotsb$ such that, for all $i$, the equational theory of $\mathfrak A_i$ is undecidable and the equational theory of $\mathfrak B_i$ is decidable.
Key words: variety of rings, finitely based variety, equational theory, decidable theory, undecidable theory.
Received: 27.10.1999
Bibliographic databases:
UDC: 512+519.4
Language: Russian
Citation: V. Yu. Popov, “On Some Algorithmic Problems Related to Varieties of Nonassociative Rings”, Mat. Tr., 3:2 (2000), 146–170; Siberian Adv. Math., 11:2 (2001), 60–82
Citation in format AMSBIB
\Bibitem{Pop00}
\by V.~Yu.~Popov
\paper On Some Algorithmic Problems Related to Varieties of Nonassociative Rings
\jour Mat. Tr.
\yr 2000
\vol 3
\issue 2
\pages 146--170
\mathnet{http://mi.mathnet.ru/mt170}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1806286}
\zmath{https://zbmath.org/?q=an:0987.17001|0967.17001}
\transl
\jour Siberian Adv. Math.
\yr 2001
\vol 11
\issue 2
\pages 60--82
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические труды Siberian Advances in Mathematics
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    Abstract page:165
    Full-text PDF :75
    First page:1
     
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