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Mat. Sb., 2000, Volume 191, Number 3, Pages 143–160 (Mi msb467)  

This article is cited in 37 scientific papers (total in 37 papers)

Examples of $T$-spaces with an infinite basis

V. V. Shchigolev

M. V. Lomonosov Moscow State University

Abstract: This work is devoted to the construction of $T$-spaces with an infinite basis over a field of finite characteristic and over some other rings. Examples of $T$-spaces are given that are generated by polynomials in two variables or by polynomials of bounded degree in each variable.

DOI: https://doi.org/10.4213/sm467

Full text: PDF file (278 kB)
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English version:
Sbornik: Mathematics, 2000, 191:3, 459–476

Bibliographic databases:

UDC: 512.5
MSC: Primary 16R10; Secondary 16R50
Received: 23.02.1999

Citation: V. V. Shchigolev, “Examples of $T$-spaces with an infinite basis”, Mat. Sb., 191:3 (2000), 143–160; Sb. Math., 191:3 (2000), 459–476

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    This publication is cited in the following articles:
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    2. 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
    3. 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
    4. Gupta C.K., Krasilnikov A.N., “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
    5. 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
    6. A. V. Grishin, “Multiplicities and indices of representability of non-matrix varieties of algebras”, Russian Math. Surveys, 58:6 (2003), 1198–1199  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. 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  mathscinet  zmath  isi
    8. 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
    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. 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
    11. 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
    12. Grishin A.V., Shchigolev V.V., “$T$-spaces and their applications”, J. Math. Sci. (N. Y.), 134:1 (2006), 1799–1878  crossref  mathscinet  zmath  scopus  scopus  scopus
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    14. A. V. Grishin, L. M. Surmina, “On $T$-spaces of $n$-words over a field of characteristic $p>0$”, Russian Math. Surveys, 62:4 (2007), 802–803  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    15. A. V. Grishin, L. M. Tsybulya, “Two theorems on the structure of a relatively free Grassmann algebra”, Russian Math. Surveys, 63:4 (2008), 782–784  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. A. V. Grishin, “On T-spaces and related concepts and results”, J. Math. Sci., 163:6 (2009), 677–681  mathnet  crossref  mathscinet
    17. 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
    18. 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
    19. 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
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    21. Brandao Antonio Pereira J., Koshlukov P., Krasilnikov A., da Silva E.A., “The Central Polynomials for the Grassmann Algebra”, Israel J Math, 179:1 (2010), 127–144  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    22. C. Bekh-Ochir, S. A. Rankin, “Examples of associative algebras for which the T-space of central polynomials is not finitely based”, Isr. J. Math, 186:1 (2011), 333  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    23. C. Bekh-Ochir, S.A. Rankin, “On a conjecture of V.V. Shchigolev”, Journal of Algebra, 330:1 (2011), 314  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    24. C. BEKH-OCHIR, S. A. RANKIN, “ON A PROBLEM OF A. V. GRISHIN”, J. Algebra Appl, 11:01 (2012), 1250020  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    25. 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
    26. A. V. Grishin, “On $T$-spaces in a relatively free two-generated Lie nilpotent associative algebra of index $4$”, J. Math. Sci., 191:5 (2013), 686–690  mathnet  crossref
    27. 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
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    31. 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
    32. 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
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