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Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 5, Pages 191–224 (Mi izv362)  

This article is cited in 15 scientific papers (total in 15 papers)

The finite basis property of $T$-spaces over fields of characteristic zero

V. V. Shchigolev

M. V. Lomonosov Moscow State University

Abstract: In this paper we prove that any $T$-space over a field of characteristic zero has a finite basis. This result generalizes Kemer's theorem on the existence of a finite basis for any system of associative identities over a field of characteristic zero.


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English version:
Izvestiya: Mathematics, 2001, 65:5, 1041–1071

Bibliographic databases:

MSC: Primary 16R10; Secondary 16R50
Received: 02.06.2000

Citation: V. V. Shchigolev, “The finite basis property of $T$-spaces over fields of characteristic zero”, Izv. RAN. Ser. Mat., 65:5 (2001), 191–224; Izv. Math., 65:5 (2001), 1041–1071

Citation in format AMSBIB
\by V.~V.~Shchigolev
\paper The finite basis property of $T$-spaces over fields of characteristic zero
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 5
\pages 191--224
\jour Izv. Math.
\yr 2001
\vol 65
\issue 5
\pages 1041--1071

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    This publication is cited in the following articles:
    1. Shchigolev V.V., “On the stabilization problem for submodules of Specht modules”, Journal of Algebra, 251:2 (2002), 790–812  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. V. Grishin, “Model algebras, multiplicities, and representability indices of varieties of associative algebras”, Sb. Math., 195:1 (2004), 1–18  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. 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
    4. A. V. Grishin, “On T-spaces and related concepts and results”, J. Math. Sci., 163:6 (2009), 677–681  mathnet  crossref  mathscinet
    5. L. M. Tsybulya, “Theorems on equalization and monomiality in a relatively free Grassmann algebra”, J. Math. Sci., 163:6 (2009), 759–773  mathnet  crossref  mathscinet  elib  elib
    6. Bekh-Ochir Ch., Riley D., “On the Grassmann T-space”, Journal of Algebra and Its Applications, 7:3 (2008), 319–336  crossref  mathscinet  zmath  isi  scopus
    7. A. V. Grishin, L. M. Tsybulya, “On the multiplicative and $T$-space structure of the relatively free Grassmann algebra”, Sb. Math., 200:9 (2009), 1299–1338  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. 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
    9. A. Ya. Belov, “The local finite basis property and local representability of varieties of associative rings”, Izv. Math., 74:1 (2010), 1–126  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. Aljadeff E., Kanel-Belov A., “Representability and Specht problem for G-graded algebras”, Advances in Mathematics, 225:5 (2010), 2391–2428  crossref  mathscinet  zmath  isi  scopus
    11. Bekh-Ochir C., Rankin S.A., “Examples of associative algebras for which the T-space of central polynomials is not finitely based”, Israel J Math, 186:1 (2011), 333–347  crossref  mathscinet  zmath  isi  elib  scopus
    12. Dimas José Gonçalves, Alexei Krasilnikov, Irina Sviridova, “Limit T-subspaces and the central polynomials in n variables of the Grassmann algebra”, Journal of Algebra, 371 (2012), 156  crossref  mathscinet  zmath  isi  scopus
    13. D.J.osé Gonçalves, Alexei Krasilnikov, Irina Sviridova, “Limit T-subalgebras in free associative algebras”, Journal of Algebra, 412 (2014), 264  crossref  mathscinet  zmath  scopus
    14. Galina Deryabina, Alexei Krasilnikov, “The subalgebra of graded central polynomials of an associative algebra”, Journal of Algebra, 425 (2015), 313  crossref  mathscinet  zmath  scopus
    15. KanelBelov A. Karasik Y. Rowen L., “Computational Aspects of Polynomial Identities: Vol 1, Kemer'S Theorems, 2Nd Edition”, Computational Aspects of Polynomial Identities: Vol 1, Kemer'S Theorems, 2Nd Edition, Monographs and Research Notes in Mathematics, 16, Crc Press-Taylor & Francis Group, 2016, 1–407  mathscinet  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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