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Mat. Sb., 2000, Volume 191, Number 3, Pages 13–24 (Mi msb460)  

This article is cited in 35 scientific papers (total in 35 papers)

Counterexamples to the Specht problem

A. Ya. Belov

M. V. Lomonosov Moscow State University

Abstract: The present paper is devoted to the construction of infinitely based varieties of associative algebras over an infinite field of arbitrary positive characteristic.


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English version:
Sbornik: Mathematics, 2000, 191:3, 329–340

Bibliographic databases:

UDC: 512.5
MSC: Primary 16R10; Secondary 16R40
Received: 29.10.1998 and 13.10.1999

Citation: A. Ya. Belov, “Counterexamples to the Specht problem”, Mat. Sb., 191:3 (2000), 13–24; Sb. Math., 191:3 (2000), 329–340

Citation in format AMSBIB
\by A.~Ya.~Belov
\paper Counterexamples to the~Specht problem
\jour Mat. Sb.
\yr 2000
\vol 191
\issue 3
\pages 13--24
\jour Sb. Math.
\yr 2000
\vol 191
\issue 3
\pages 329--340

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    This publication is cited in the following articles:
    1. V. V. Shchigolev, “The finite basis property of $T$-spaces over fields of characteristic zero”, Izv. Math., 65:5 (2001), 1041–1071  mathnet  crossref  crossref  mathscinet  zmath
    2. Gupta C.K., Krasilnikov A.N., “A simple example of a non-finitely based system of polynomial identities”, Comm. Algebra, 30:10 (2002), 4851–4866  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    3. Gupta C.K., “A non-finitely based system of polynomial identities which contains the identity $x^6=0$”, Q. J. Math., 53:2 (2002), 173–183  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    4. N. I. Sandu, “Infinite Independent Systems of Identities of an Associative Algebra over an Infinite Field of Characteristic Two”, Math. Notes, 74:4 (2003), 569–577  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Gupta C.K., Krasilnikov A., “The finite basis question for varieties of groups—some recent results”, Illinois J. Math., 47:1-2, Special issue in honor of Reinhold Baer (1902–1979) (2003), 273–283  crossref  mathscinet  zmath  isi
    6. Jackson M., “Semilattices with closure”, Algebra Universalis, 52:1 (2004), 1–37  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    7. Drensky V., “Polynomial identity rings - Part A - Combinatorial aspects in PI-rings”, Polynomial Identity Rings, Advanced Courses in Mathematics Crm Barcelona, 2004, 1  mathscinet  zmath  isi
    8. A. N. Vaulin, “On one variety of alternative algebras”, J. Math. Sci., 140:2 (2007), 191–199  mathnet  crossref  mathscinet  zmath  elib  elib
    9. E. A. Kireeva, A. N. Krasilnikov, “On Some Extremal Varieties of Associative Algebras”, Math. Notes, 78:4 (2005), 503–517  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. 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  scopus
    11. E. A. Kireeva, “Limit T-spaces”, J. Math. Sci., 152:4 (2008), 540–557  mathnet  crossref  mathscinet  zmath
    12. A. Ya. Belov, “On Rings Asymptotically Close to Associative Rings”, Siberian Adv. Math., 17:4 (2007), 227–267  mathnet  crossref  mathscinet  elib
    13. Aladova E.V., Krasilnikov A.N., “Polynomial identities in nil-algebras”, Trans. Amer. Math. Soc., 361:11 (2009), 5629–5646  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    14. Silkin N., “On Finite Basis Property for Joins of Varieties of Associative Rings”, Communications in Algebra, 38:9 (2010), 3187–3205  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    15. Belov-Kanel A., Rowen L., Vishne U., “Structure of Zariski-Closed Algebras”, Transactions of the American Mathematical Society, 362:9 (2010), 4695–4734  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    16. 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
    17. C. Bekh-Ochir, S. A. Rankin, “The Identities and the Central Polynomials of the Infinite Dimensional Unitary Grassmann Algebra Over a Finite Field”, Comm. in Algebra, 39:3 (2011), 819  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    18. Alexei Belov-Kanel, Louis Rowen, Uzi Vishne, “Application of Full Quivers of Representations of Algebras, to Polynomial Identities”, Communications in Algebra, 39:12 (2011), 4536  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    19. Kanel-Belov A., Malev S., Rowen L., “The Images of Non-Commutative Polynomials Evaluated on 2 X 2 Matrices”, Proc Amer Math Soc, 140:2 (2012), 465–478  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    20. 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  scopus  scopus
    21. Belov-Kanel A. Rowen L.H. Vishne U., “Full Quivers of Representations of Algebras”, Trans. Am. Math. Soc., 364:10 (2012), 5525–5569  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    22. Belov-Kanel A. Rowen L.H. Vishne U., “Pi-Varieties Associated to Full Quivers of Representations of Algebras”, Trans. Am. Math. Soc., 365:5 (2013), 2681–2722  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    23. G. S. Deryabina, A. N. Krasilnikov, “A Non-Finitely-Based Variety of Centrally Metabelian Pointed Groups”, Math. Notes, 95:5 (2014), 743–746  mathnet  crossref  crossref  mathscinet  isi  elib
    24. 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  scopus  scopus
    25. Galina Deryabina, Alexei Krasilnikov, “The subalgebra of graded central polynomials of an associative algebra”, Journal of Algebra, 425 (2015), 313  crossref  mathscinet  zmath  scopus  scopus  scopus
    26. Lucio Centrone, V.R.i.T.omaz da Silva, “On <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="" xmlns:xs="" xmlns:xsi="" xmlns="" xmlns:ja="" xmlns:mml="" xmlns:tb="" xmlns:sb="" xmlns:ce="" xmlns:xlink="" xmlns:cals="" xmlns:sa=""><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">Z</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math>-graded identities of <mml:math altimg="si2.gif" overflow="scroll" xmlns:xocs="http://w”, Linear Algebra and its Applications, 471 (2015), 469  crossref  mathscinet  zmath  scopus  scopus  scopus
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    28. Belov-Kanel A. Rowen L. Vishne U., “Specht'S Problem For Associative Affine Algebras Over Commutative Noetherian Rings”, Trans. Am. Math. Soc., 367:8 (2015), 5553–5596  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    29. O. V. Shashkov, “The join of varieties with associative-commutative intersection of bounded index”, Siberian Math. J., 56:3 (2015), 557–564  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    30. 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
    31. Centrone L., Tomaz da Silva V.R., “A note on graded polynomial identities for tensor products by the Grassmann algebra in positive characteristic”, Int. J. Algebr. Comput., 26:6 (2016), 1125–1140  crossref  mathscinet  zmath  isi  scopus
    32. S. V. Pchelintsev, “Identities of metabelian alternative algebras”, Siberian Math. J., 58:4 (2017), 693–710  mathnet  crossref  crossref  isi  elib  elib
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    34. Centrone L., Martino F., Souza Manuela da Silva, “Specht Property For Some Varieties of Jordan Algebras of Almost Polynomial Growth”, J. Algebra, 521 (2019), 137–165  crossref  mathscinet  zmath  isi  scopus
    35. Alexei  Kanel-Belov, Sergey Malev, Louis Rowen, Roman Yavich, “Evaluations of Noncommutative Polynomials on Algebras: Methods and Problems, and the L'vov–Kaplansky Conjecture”, SIGMA, 16 (2020), 071, 61 pp.  mathnet  crossref
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