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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.


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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

Citation in format AMSBIB
\by V.~V.~Shchigolev
\paper Examples of $T$-spaces with an~infinite basis
\jour Mat. Sb.
\yr 2000
\vol 191
\issue 3
\pages 143--160
\jour Sb. Math.
\yr 2000
\vol 191
\issue 3
\pages 459--476

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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
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    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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    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
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