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Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 2, Pages 379–397 (Mi izv1246)  

This article is cited in 4 scientific papers (total in 4 papers)

The structure of models and a decidability criterion for complete theories of finite-dimensional algebras

A. G. Myasnikov


Abstract: The author gives an algebraic description of models of the theory $\operatorname{Th}(R)$ and a criterion for its decidability for an arbitrary (not necessarily associative, and possibly without an identity) finite-dimensional $k$-algebra over a field $k$ of arbitrary characteristic. This description is based on the solution of the following purely algebraic problem: how completely can the structure of a $k$-module $R$ be recovered, knowing only the ring operations of $R$?
Bibliography: 20 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1990, 34:2, 389–407

Bibliographic databases:

UDC: 512.54+510.67
MSC: 03C60, 16A46
Received: 26.03.1987

Citation: A. G. Myasnikov, “The structure of models and a decidability criterion for complete theories of finite-dimensional algebras”, Izv. Akad. Nauk SSSR Ser. Mat., 53:2 (1989), 379–397; Math. USSR-Izv., 34:2 (1990), 389–407

Citation in format AMSBIB
\Bibitem{Mya89}
\by A.~G.~Myasnikov
\paper The structure of models and a~decidability criterion for complete theories of finite-dimensional algebras
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 2
\pages 379--397
\mathnet{http://mi.mathnet.ru/izv1246}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=998302}
\zmath{https://zbmath.org/?q=an:0702.03014}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 34
\issue 2
\pages 389--407
\crossref{https://doi.org/10.1070/IM1990v034n02ABEH000655}


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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. K. I. Beidar, A. V. Mikhalev, G. E. Puninskii, “Logicheskie aspekty teorii kolets i modulei”, Fundament. i prikl. matem., 1:1 (1995), 1–62  mathnet  mathscinet  zmath  elib
    2. SERGUEI LIOUTIKOV, ALEXEI MYASNIKOV, “Centroids of groups”, jgth, 3:2 (2000), 177  crossref  mathscinet  zmath  elib
    3. A. G. Miasnikov, M. Sohrabi, “Groups elementarily equivalent to a free 2-nilpotent group of finite rank”, Algebra and Logic, 48:2 (2009), 115–139  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    4. Myasnikov A. Nikolaev A., “Verbal subgroups of hyperbolic groups have infinite width”, J. Lond. Math. Soc.-Second Ser., 90:2 (2014), 573–591  crossref  mathscinet  zmath  isi  scopus
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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