|
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.
DOI:
https://doi.org/10.4213/sm460
 Full text:
PDF file (250 kB)
References:
PDF file
HTML file
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
\Bibitem{Bel00}
\by A.~Ya.~Belov
\paper Counterexamples to the~Specht problem
\jour Mat. Sb.
\yr 2000
\vol 191
\issue 3
\pages 13--24
\mathnet{http://mi.mathnet.ru/msb460}
\crossref{https://doi.org/10.4213/sm460}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1773251}
\zmath{https://zbmath.org/?q=an:0960.16029}
\transl
\jour Sb. Math.
\yr 2000
\vol 191
\issue 3
\pages 329--340
\crossref{https://doi.org/10.1070/sm2000v191n03ABEH000460}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000088115700002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0034338841}
Linking options:
http://mi.mathnet.ru/eng/msb460https://doi.org/10.4213/sm460 http://mi.mathnet.ru/eng/msb/v191/i3/p13
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:
-
V. V. Shchigolev, “The finite basis property of $T$-spaces over fields of characteristic zero”, Izv. Math., 65:5 (2001), 1041–1071
 -
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
 -
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
-
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
-
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
-
Jackson M., “Semilattices with closure”, Algebra Universalis, 52:1 (2004), 1–37
-
Drensky V., “Polynomial identity rings - Part A - Combinatorial aspects in PI-rings”, Polynomial Identity Rings, Advanced Courses in Mathematics Crm Barcelona, 2004, 1
-
A. N. Vaulin, “On one variety of alternative algebras”, J. Math. Sci., 140:2 (2007), 191–199
-
E. A. Kireeva, A. N. Krasilnikov, “On Some Extremal Varieties of Associative Algebras”, Math. Notes, 78:4 (2005), 503–517
-
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
-
E. A. Kireeva, “Limit T-spaces”, J. Math. Sci., 152:4 (2008), 540–557
-
A. Ya. Belov, “On Rings Asymptotically Close to Associative Rings”, Siberian Adv. Math., 17:4 (2007), 227–267
-
Aladova E.V., Krasilnikov A.N., “Polynomial identities in nil-algebras”, Trans. Amer. Math. Soc., 361:11 (2009), 5629–5646
-
Silkin N., “On Finite Basis Property for Joins of Varieties of Associative Rings”, Communications in Algebra, 38:9 (2010), 3187–3205
-
Belov-Kanel A., Rowen L., Vishne U., “Structure of Zariski-Closed Algebras”, Transactions of the American Mathematical Society, 362:9 (2010), 4695–4734
-
A. Ya. Belov, “The local finite basis property and local representability of varieties of associative rings”, Izv. Math., 74:1 (2010), 1–126
 -
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
-
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
-
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
-
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
-
Belov-Kanel A. Rowen L.H. Vishne U., “Full Quivers of Representations of Algebras”, Trans. Am. Math. Soc., 364:10 (2012), 5525–5569
-
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
-
G. S. Deryabina, A. N. Krasilnikov, “A Non-Finitely-Based Variety of Centrally Metabelian Pointed Groups”, Math. Notes, 95:5 (2014), 743–746
-
D.J.osé Gonçalves, Alexei Krasilnikov, Irina Sviridova, “Limit T-subalgebras in free associative algebras”, Journal of Algebra, 412 (2014), 264
-
Galina Deryabina, Alexei Krasilnikov, “The subalgebra of graded central polynomials of an associative algebra”, Journal of Algebra, 425 (2015), 313
-
Lucio Centrone, V.R.i.T.omaz da Silva, “On <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><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
-
Alexey Kuz'min, “Nonfinitely Based Varieties of Right Alternative Metabelian Algebras”, Communications in Algebra, 43:8 (2015), 3169
-
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
-
O. V. Shashkov, “The join of varieties with associative-commutative intersection of bounded index”, Siberian Math. J., 56:3 (2015), 557–564
-
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
-
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
-
S. V. Pchelintsev, “Identities of metabelian alternative algebras”, Siberian Math. J., 58:4 (2017), 693–710
-
Fidelis C., Diniz D., Koshlukov P., “Embeddings For the Jordan Algebra of a Bilinear Form”, Adv. Math., 337 (2018), 294–316
-
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
-
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.
|
| Number of views: |
| This page: | 484 | | Full text: | 165 | | References: | 38 | | First page: | 3 |
|
Terms of Use