RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sibirsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Sibirsk. Mat. Zh., 2017, Volume 58, Number 4, Pages 894–915 (Mi smj2907)  

This article is cited in 1 scientific paper (total in 1 paper)

Identities of metabelian alternative algebras

S. V. Pchelintsevab

a Financial University Under the Government of the Russian Federation Moscow, Russia
b Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: We study metabelian alternative (in particular, associative) algebras over a field of characteristic 0. We construct additive bases of the free algebras of mentioned varieties, describe some centers of these algebras, compute the values of the sequence of codimensions of corresponding $T$-ideals, and find unitarily irreducible components of the decomposition of mentioned varieties into a union and their bases of identities. In particular, we find a basis of identities for the metabelian alternative Grassmann algebra. We prove that the free algebra of a variety that is generated by the metabelian alternative Grassmann algebra possesses the zero associative center.

Keywords: free algebra, metabelian algebra, center of an algebra, sequence of codimensions of a Tideal, union of varieties.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00756
The author was supported by the Russian Foundation for Basic Research (Grant 16-01-00756).


DOI: https://doi.org/10.17377/smzh.2017.58.416

Full text: PDF file (392 kB)
References: PDF file   HTML file

English version:
Siberian Mathematical Journal, 2017, 58:4, 693–710

Bibliographic databases:

UDC: 512.552.5+512.572
MSC: 35R30
Received: 01.10.2016

Citation: S. V. Pchelintsev, “Identities of metabelian alternative algebras”, Sibirsk. Mat. Zh., 58:4 (2017), 894–915; Siberian Math. J., 58:4 (2017), 693–710

Citation in format AMSBIB
\Bibitem{Pch17}
\by S.~V.~Pchelintsev
\paper Identities of metabelian alternative algebras
\jour Sibirsk. Mat. Zh.
\yr 2017
\vol 58
\issue 4
\pages 894--915
\mathnet{http://mi.mathnet.ru/smj2907}
\crossref{https://doi.org/10.17377/smzh.2017.58.416}
\elib{http://elibrary.ru/item.asp?id=29947459}
\transl
\jour Siberian Math. J.
\yr 2017
\vol 58
\issue 4
\pages 693--710
\crossref{https://doi.org/10.1134/S0037446617040164}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000408727100016}
\elib{http://elibrary.ru/item.asp?id=31064052}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85028577186}


Linking options:
  • http://mi.mathnet.ru/eng/smj2907
  • http://mi.mathnet.ru/eng/smj/v58/i4/p894

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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, “Asymptotics of the Codimensions $c_n$ in the Algebra $F^{(7)}$”, Math. Notes, 104:1 (2018), 22–28  mathnet  crossref  crossref  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
    Number of views:
    This page:82
    Full text:14
    References:18
    First page:4

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020