Matematicheskii Sbornik. Novaya Seriya
General information
Latest issue
Forthcoming papers
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Mat. Sb.:

Personal entry:
Save password
Forgotten password?

Mat. Sb. (N.S.), 1983, Volume 122(164), Number 1(9), Pages 31–40 (Mi msb2271)  

This article is cited in 17 scientific papers (total in 17 papers)

Finitely generated special Jordan and alternative $PI$-algebras

I. P. Shestakov

Abstract: The author explores the question of whether identities related to special Jordan and alternative $PI$-algebras exist in associative algebras. It is proved that if $A$ is a finitely generated special Jordan (alternative) $PI$-algebra, then the universal associative enveloping algebra $S(A)$ (respectively, the universal algebra $\mathscr R(A)$ for right alternative representations) of algebra $A$ is also a $PI$-algebra. As a corollary it is proved that the upper nilradical of a finitely generated special Jordan or alternative $PI$-algebra over a Noetherian ring is nilpotent. A similar result holds for the Zhevlakov radical of a finitely generated free alternative algebra. In addition, a criterion is obtained for local associator nilpotence of an alternative algebra.
Bibliography: 19 titles.

Full text: PDF file (682 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1985, 50:1, 31–40

Bibliographic databases:

UDC: 519.48
MSC: Primary 17C25; Secondary 17C10, 16A68
Received: 18.06.1982

Citation: I. P. Shestakov, “Finitely generated special Jordan and alternative $PI$-algebras”, Mat. Sb. (N.S.), 122(164):1(9) (1983), 31–40; Math. USSR-Sb., 50:1 (1985), 31–40

Citation in format AMSBIB
\by I.~P.~Shestakov
\paper Finitely generated special Jordan and alternative $PI$-algebras
\jour Mat. Sb. (N.S.)
\yr 1983
\vol 122(164)
\issue 1(9)
\pages 31--40
\jour Math. USSR-Sb.
\yr 1985
\vol 50
\issue 1
\pages 31--40

Linking options:

    SHARE: FaceBook Twitter Livejournal

    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. S. V. Pchelintsev, “A theorem on height for alternative algebras”, Math. USSR-Sb., 52:2 (1985), 541–551  mathnet  crossref  mathscinet  zmath
    2. S. V. Pchelintsev, “Prime algebras and absolute zero divisors”, Math. USSR-Izv., 28:1 (1987), 79–98  mathnet  crossref  mathscinet  zmath
    3. Yu. A. Medvedev, “Representations of finitely generated Jordan PI-algebras”, Math. USSR-Izv., 32:1 (1989), 63–76  mathnet  crossref  mathscinet  zmath
    4. A. Ya. Belov, “On a Shirshov basis of relatively free algebras of complexity $n$”, Math. USSR-Sb., 63:2 (1989), 363–374  mathnet  crossref  mathscinet  zmath
    5. E. I. Zel'manov, I. P. Shestakov, “Prime alternative superalgebras and the nilpotence of the radical of a free alternative algebra”, Math. USSR-Izv., 37:1 (1991), 19–36  mathnet  crossref  mathscinet  zmath  adsnasa
    6. V. T. Markov, “On matrix algebras with two generators and on embedding $PI$-algebras”, Russian Math. Surveys, 47:4 (1992), 216–217  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. Plamen Koshlukov, “Polynomial identities for Jordan pairs”, Communications in Algebra, 22:8 (1994), 2749  crossref  mathscinet  zmath
    8. M. M. Babikov, “A criterion for the solvability of alternative algebras”, Math. Notes, 57:3 (1995), 229–234  mathnet  crossref  mathscinet  zmath  isi  elib
    9. José A. Anquela, Teresa Cortés, Fernando Montaner, “The structure of primitive quadratic Jordan algebras”, Journal of Algebra, 172:2 (1995), 530  crossref  mathscinet  zmath
    10. S. V. Pchelintsev, “Nilpotency of the alternator ideal of a finitely generated binary $(-1,1)$-algebra”, Siberian Math. J., 45:2 (2004), 356–375  mathnet  crossref  mathscinet  zmath  isi  elib
    11. A. Ya. Belov, “Burnside-type problems, theorems on height, and independence”, J. Math. Sci., 156:2 (2009), 219–260  mathnet  crossref  mathscinet  zmath  elib  elib
    12. A. Ya. Belov, “On Rings Asymptotically Close to Associative Rings”, Siberian Adv. Math., 17:4 (2007), 227–267  mathnet  crossref  mathscinet  elib
    13. Shestakov I., Zhukavets N., “The Free Alternative Superalgebra on One Odd Generator”, Int. J. Algebr. Comput., 17:5-6 (2007), 1215–1247  crossref  mathscinet  zmath  isi  elib
    14. Zhukavets N.M., Shestakov I.P., “A Base of the Free Alternative Superalgebra on One Odd Generator”, Dokl. Math., 78:2 (2008), 693–695  mathnet  crossref  mathscinet  zmath  isi  elib
    15. Shestakov I.P., Kornev A.I., “On the Radical of a Free Malcev Algebra”, Proc. Amer. Math. Soc., 140:9 (2012), 3049–3054  crossref  mathscinet  zmath  isi  elib
    16. 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
    17. Pchelintsev S.V., “Proper identities of finitely generated commutative alternative algebras”, J. Algebra, 470 (2017), 425–440  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:414
    Full text:109
    First page:2

    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2022