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Fundam. Prikl. Mat., 1999, Volume 5, Issue 1, Pages 307–312 (Mi fpm378)  

This article is cited in 32 scientific papers (total in 32 papers)

Examples of infinitely based T-ideals

V. V. Shchigolev

M. V. Lomonosov Moscow State University

Abstract: In the paper an example of an infinitely based T-ideal is built. The given example is monomial.

Full text: PDF file (259 kB)

Bibliographic databases:
UDC: 519.48
Received: 01.11.1998

Citation: V. V. Shchigolev, “Examples of infinitely based T-ideals”, Fundam. Prikl. Mat., 5:1 (1999), 307–312

Citation in format AMSBIB
\Bibitem{Shc99}
\by V.~V.~Shchigolev
\paper Examples of infinitely based T-ideals
\jour Fundam. Prikl. Mat.
\yr 1999
\vol 5
\issue 1
\pages 307--312
\mathnet{http://mi.mathnet.ru/fpm378}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1799533}
\zmath{https://zbmath.org/?q=an:0968.16008}


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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. 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. Shchigolev, VV, “Construction of non-finitely based T-ideals”, Communications in Algebra, 29:9 (2001), 3935  crossref  mathscinet  zmath  isi
    3. Giambruno, A, “On the identities of the Grassmann algebras in characteristic p > 0”, Israel Journal of Mathematics, 122 (2001), 305  crossref  mathscinet  zmath  isi
    4. 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
    5. Gupta, CK, “A non-finitely based system of polynomial identities which contains the identity x(6)=0”, Quarterly Journal of Mathematics, 53 (2002), 173  crossref  mathscinet  isi
    6. 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
    7. 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
    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. 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
    10. 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
    11. Crvenkovic, S, “A locally finite variety of rings with an undecidable equational theory”, Quarterly Journal of Mathematics, 57 (2006), 297  crossref  mathscinet  zmath  isi
    12. Drensky, V, “Grobner bases of ideals invariant under endomorphisms”, Journal of Symbolic Computation, 41:7 (2006), 835  crossref  mathscinet  zmath  isi
    13. E. A. Kireeva, “Limit T-spaces”, J. Math. Sci., 152:4 (2008), 540–557  mathnet  crossref  mathscinet  zmath
    14. A. Ya. Belov, “On Rings Asymptotically Close to Associative Rings”, Siberian Adv. Math., 17:4 (2007), 227–267  mathnet  crossref  mathscinet  elib
    15. 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
    16. 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
    17. 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
    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
    20. Klyachko A.A., Menshova E.V., “The identities of additive binary arithmetics”, Electron J Combin, 19:1 (2012), P40  mathscinet  zmath  isi
    21. 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
    22. Edmond W. H. Lee, “Maximal Specht varieties of monoids”, Mosc. Math. J., 12:4 (2012), 787–802  mathnet  mathscinet
    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. Concalves D.J. Krasilnikov A. Sviridova I., “Limit T-Subalgebras in Free Associative Algebras”, J. Algebra, 412 (2014), 264–280  crossref  mathscinet  isi
    25. M. I. Kharitonov, “Otsenki, svyazannye s teoremoi Shirshova o vysote”, Chebyshevskii sb., 15:4 (2014), 55–123  mathnet
    26. 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
    27. 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
    28. 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
    29. M. I. Kharitonov, “The estimate of the number of permutationally-ordered sets”, Moscow University Mathematics Bulletin, 70:3 (2015), 125–129  mathnet  crossref  mathscinet
    30. 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
    31. S. V. Pchelintsev, “Identities of the model algebra of multiplicity 2”, Siberian Math. J., 59:6 (2018), 1105–1124  mathnet  crossref  crossref  isi
    32. 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
  • Фундаментальная и прикладная математика
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