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Izv. Akad. Nauk SSSR Ser. Mat., 1973, Volume 37, Issue 3, Pages 483–501 (Mi izv2275)  

This article is cited in 22 scientific papers (total in 22 papers)

On a problem of Kaplanskii

Yu. P. Razmyslov


Abstract: In this article we construct for any natural number $n$ an associative multilinear polynomial whose values on matrices of order $n$ are scalar matrices at least one of which is nonzero.

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English version:
Mathematics of the USSR-Izvestiya, 1973, 7:3, 479–496

Bibliographic databases:

UDC: 519.4
MSC: Primary 16A42; Secondary 16A68, 17B45
Received: 12.05.1972

Citation: Yu. P. Razmyslov, “On a problem of Kaplanskii”, Izv. Akad. Nauk SSSR Ser. Mat., 37:3 (1973), 483–501; Math. USSR-Izv., 7:3 (1973), 479–496

Citation in format AMSBIB
\Bibitem{Raz73}
\by Yu.~P.~Razmyslov
\paper On a~problem of Kaplanskii
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1973
\vol 37
\issue 3
\pages 483--501
\mathnet{http://mi.mathnet.ru/izv2275}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=338063}
\zmath{https://zbmath.org/?q=an:0314.16016}
\transl
\jour Math. USSR-Izv.
\yr 1973
\vol 7
\issue 3
\pages 479--496
\crossref{https://doi.org/10.1070/IM1973v007n03ABEH001952}


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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. T. Markov, “On the dimension of noncommutative affine algebras”, Math. USSR-Izv., 7:2 (1973), 281–285  mathnet  crossref  mathscinet  zmath
    2. Yu. P. Razmyslov, “Trace identities of full matrix algebras over a field of characteristic zero”, Math. USSR-Izv., 8:4 (1974), 727–760  mathnet  crossref  mathscinet  zmath
    3. V. T. Markov, “O koltsakh chastnykh polupervichnykh $PI$-kolets i nesokratimykh podpryamykh proizvedenii”, UMN, 30:4(184) (1975), 253–254  mathnet  mathscinet  zmath
    4. Yu. P. Razmyslov, “On a problem of Hall and Higman”, Math. USSR-Izv., 13:1 (1979), 133–146  mathnet  crossref  mathscinet  zmath  isi
    5. N. I. Dubrovin, “Maximal orders in a finite-dimensional central simple algebra over a valuation ring of height 1”, Math. USSR-Sb., 36:4 (1980), 483–493  mathnet  crossref  mathscinet  zmath  isi
    6. V. K. Kharchenko, “The actions of groups and Lie algebras on non-commutative rings”, Russian Math. Surveys, 35:2 (1980), 77–104  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. Yu. P. Razmyslov, “Central polynomials in irreducible representations of a semisimple Lie algebra”, Math. USSR-Sb., 50:1 (1985), 99–124  mathnet  crossref  mathscinet  zmath
    8. Patrick Halpin, “Central and weak identities for matrices”, Communications in Algebra, 11:19 (1983), 2237  crossref
    9. C Procesi, “Computing with 2 × 2 matrices”, Journal of Algebra, 87:2 (1984), 342  crossref
    10. Yu. P. Razmyslov, “Trace identities and central polynomials in the matrix superalgebras $M_{n,k}$”, Math. USSR-Sb., 56:1 (1987), 187–206  mathnet  crossref  mathscinet  zmath
    11. Patrick Halpin, “Symmetric T-ideals”, Linear Algebra and its Applications, 79 (1986), 53  crossref
    12. Siamack Bondari, “Constructing the polynomlal identities and central identities of degree <9 of 3 × 3 matrices”, Linear Algebra and its Applications, 258 (1997), 233  crossref
    13. Y. Barnea, A. Shalev, E. I. Zelmanov, “Graded subalgebras of affine Kac-Moody algebras”, Isr J Math, 104:1 (1998), 321  crossref  mathscinet  zmath  isi
    14. Kh. D. Ikramov, “The quasidiagonalizability of oblique projectors as a particular case of the noncommutative spectral theorem”, Comput. Math. Math. Phys., 40:8 (2000), 1077–1084  mathnet  mathscinet  zmath
    15. I. N. Balaba, “Graded prime PI-algebras”, J. Math. Sci., 128:6 (2005), 3345–3349  mathnet  crossref  mathscinet  zmath  elib  elib
    16. A. Ya. Belov, “No associative $PI$-algebra coincides with its commutant”, Siberian Math. J., 44:6 (2003), 969–980  mathnet  crossref  mathscinet  zmath  isi  elib
    17. A. V. Grishin, “On T-spaces and related concepts and results”, J. Math. Sci., 163:6 (2009), 677–681  mathnet  crossref  mathscinet
    18. Luís Felipe Gonçalves Fonseca, “On the graded central polynomials for elementary gradings in matrix algebras”, Rend. Circ. Mat. Palermo, 2013  crossref
    19. Tatiana Bandman, Shelly Garion, Boris Kunyavskiǐ, “Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics”, centr.eur.j.math, 12:2 (2014), 175  crossref
    20. Luís.F.e.G.onçalves Fonseca, “Graded polynomial identities and central polynomials of matrices over an infinite integral domain”, Rend. Circ. Mat. Palermo, 63:3 (2014), 371  crossref
    21. Zelmanov E., “Groups With Identities”, Note Mat., 36:1 (2016), 101–113  crossref  mathscinet  isi  scopus
    22. 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
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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