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Fundam. Prikl. Mat., 1999, Volume 5, Issue 1, Pages 101–118 (Mi fpm371)  

This article is cited in 47 scientific papers (total in 47 papers)

Examples of T-spaces and T-ideals over a field of characteristic 2 without the finite basis property

A. V. Grishin

Moscow State Pedagogical University

Abstract: In this paper we construct examples of T-spaces and T-ideals over a field of characteristic 2, which do not have the finite basis property.

Full text: PDF file (935 kB)

Bibliographic databases:
UDC: 512.552.4
Received: 01.04.1998

Citation: A. V. Grishin, “Examples of T-spaces and T-ideals over a field of characteristic 2 without the finite basis property”, Fundam. Prikl. Mat., 5:1 (1999), 101–118

Citation in format AMSBIB
\Bibitem{Gri99}
\by A.~V.~Grishin
\paper Examples of T-spaces and T-ideals over a~field of characteristic~2 without the~finite basis property
\jour Fundam. Prikl. Mat.
\yr 1999
\vol 5
\issue 1
\pages 101--118
\mathnet{http://mi.mathnet.ru/fpm371}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1799541}
\zmath{https://zbmath.org/?q=an:1015.16022}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Grishin, “On non-spechtianness of the variety of associative rings that satisfy the identity x(32)=0”, Electronic Research Announcements of the American Mathematical Society, 6 (2000), 50–51  crossref  mathscinet  zmath  isi
    2. Grishin A.V., “The variety of associative rings, which satisfy the identity x(32)=0, is not specht”, Formal Power Series and Algebraic Combinatorics, 2000, 686–691  crossref  mathscinet  zmath  isi
    3. 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
    4. Shchigolev, VV, “Construction of non-finitely based T-ideals”, Communications in Algebra, 29:9 (2001), 3935  crossref  mathscinet  zmath  isi
    5. A. Giambruno, P. Koshlukov, “On the identities of the Grassmann algebras in characteristic $p>0$”, Israel Journal of Mathematics, 122 (2001), 305–316  crossref  mathscinet  zmath  isi
    6. Gupta, CK, “A simple example of a non-finitely based system of polynomial identities”, Communications in Algebra, 30:10 (2002), 4851  crossref  mathscinet  zmath  isi
    7. Gupta, CK, “A non-finitely based system of polynomial identities which contains the identity $x^6=0$”, Quarterly Journal of Mathematics, 53:2 (2002), 173–183  crossref  mathscinet  zmath  isi
    8. Gupta, CK, “The finite basis question for varieties of groups - Some recent results”, Illinois Journal of Mathematics, 47:1–2 (2003), 273  mathscinet  zmath  isi
    9. 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
    10. 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
    11. 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
    12. 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
    13. Crvenkovic, S, “A locally finite variety of rings with an undecidable equational theory”, Quarterly Journal of Mathematics, 57:3 (2006), 297–307  crossref  mathscinet  zmath  isi
    14. Drensky, V, “Grobner bases of ideals invariant under endomorphisms”, Journal of Symbolic Computation, 41:7 (2006), 835  crossref  mathscinet  zmath  isi
    15. 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
    16. E. A. Kireeva, “Limit T-spaces”, J. Math. Sci., 152:4 (2008), 540–557  mathnet  crossref  mathscinet  zmath
    17. A. Ya. Belov, “On Rings Asymptotically Close to Associative Rings”, Siberian Adv. Math., 17:4 (2007), 227–267  mathnet  crossref  mathscinet  elib
    18. 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
    19. A. V. Grishin, “On T-spaces and related concepts and results”, J. Math. Sci., 163:6 (2009), 677–681  mathnet  crossref  mathscinet
    20. 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
    21. 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
    22. Aladova E.V., Krasilnikov A.N., “Polynomial Identities in Nil-Algebras”, Transactions of the American Mathematical Society, 361:11 (2009), 5629–5646  crossref  mathscinet  zmath  isi
    23. 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
    24. 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
    25. A. V. Grishin, L. M. Tsybulya, A. A. Shokola, “On $T$-spaces and relations in relatively free, Lie nilpotent, associative algebras”, J. Math. Sci., 177:6 (2011), 868–877  mathnet  crossref  mathscinet  elib
    26. Silkin N., “On Finite Basis Property for Joins of Varieties of Associative Rings”, Comm Algebra, 38:9 (2010), 3187–3205  crossref  mathscinet  zmath  isi  elib
    27. Belov-Kanel A., Rowen L., Vishne U., “Application of Full Quivers of Representations of Algebras, to Polynomial Identities”, Comm Algebra, 39:12 (2011), 4536–4551  crossref  mathscinet  zmath  isi  elib
    28. Klyachko A.A., Menshova E.V., “The identities of additive binary arithmetics”, Electron J Combin, 19:1 (2012), P40  mathscinet  zmath  isi
    29. 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
    30. Goncalves D.J. Krasilnikov A. Sviridova I., “Limit T-Subspaces and the Central Polynomials in N Variables of the Grassmann Algebra”, J. Algebra, 371 (2012), 156–174  crossref  mathscinet  zmath  isi  elib
    31. 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
    32. Edmond W. H. Lee, “Maximal Specht varieties of monoids”, Mosc. Math. J., 12:4 (2012), 787–802  mathnet  mathscinet
    33. 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
    34. Concalves D.J. Krasilnikov A. Sviridova I., “Limit T-Subalgebras in Free Associative Algebras”, J. Algebra, 412 (2014), 264–280  crossref  mathscinet  isi
    35. M. I. Kharitonov, “Otsenki, svyazannye s teoremoi Shirshova o vysote”, Chebyshevskii sb., 15:4 (2014), 55–123  mathnet
    36. 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
    37. A. V. Grishin, S. V. Pchelintsev, “On centres of relatively free associative algebras with a Lie nilpotency identity”, Sb. Math., 206:11 (2015), 1610–1627  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    38. Kuz'min A., “on the Topological Rank of the Variety of Right Alternative Metabelian Lie-Nilpotent Algebras”, J. Algebra. Appl., 14:10 (2015), 1550144  crossref  mathscinet  zmath  isi
    39. 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
    40. Centrone L., Tomaz da Silva V.R., “on Z(2)-Graded Identities of Ut2(E) and Their Growth”, Linear Alg. Appl., 471 (2015), 469–499  crossref  mathscinet  zmath  isi  elib
    41. Deryabina G. Krasilnikov A., “the Subalgebra of Graded Central Polynomials of An Associative Algebra”, J. Algebra, 425 (2015), 313–323  crossref  mathscinet  zmath  isi  elib
    42. Kuz'min A., “Nonfinitely Based Varieties of Right Alternative Metabelian Algebras”, Commun. Algebr., 43:8 (2015), 3169–3189  crossref  mathscinet  zmath  isi
    43. M. I. Kharitonov, “The estimate of the number of permutationally-ordered sets”, Moscow University Mathematics Bulletin, 70:3 (2015), 125–129  mathnet  crossref  mathscinet
    44. S. V. Pchelintsev, “Identities of metabelian alternative algebras”, Siberian Math. J., 58:4 (2017), 693–710  mathnet  crossref  crossref  isi  elib  elib
    45. Di Vincenzo O.M. Koshlukov P. Tomaz da Silva V.R., “On Z(P)-Graded Identities and Cocharacters of the Grassmann Algebra”, Commun. Algebr., 45:1 (2017), 343–356  crossref  mathscinet  zmath  isi  scopus
    46. Fidelis C., Diniz D., Koshlukov P., “Embeddings For the Jordan Algebra of a Bilinear Form”, Adv. Math., 337 (2018), 294–316  crossref  mathscinet  zmath  isi  scopus
    47. Kireeva E. Shchigolev V., “The Nilpotence Degree of Quantum Lie Nilpotent Algebras”, Int. J. Algebr. Comput., 28:6 (2018), 1119–1128  crossref  mathscinet  zmath  isi  scopus
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