Algebra i logika
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



Algebra Logika:
Year:
Volume:
Issue:
Page:
Find






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


Algebra Logika, 2013, Volume 52, Number 6, Pages 731–768 (Mi al616)  

This article is cited in 2 scientific papers (total in 2 papers)

Almost commutative varieties of associative rings and algebras over a finite field

O. B. Finogenova

El'tsin Ural Federal University, pr. Lenina 51, Yekaterinburg, 620083, Russia

Abstract: Associative algebras over an associative commutative ring with unity are considered. A variety of algebras is said to be permutative if it satisfies an identity of the form
$$ x_1x_2\cdots x_n=x_{1\sigma}x_{2\sigma}\cdots x_{n\sigma}, $$
where $\sigma$ is a nontrivial permutation on a set $\{1,2,…,n\}$. Minimal elements in the lattice of all nonpermutative varieties are called almost permutative varieties. By Zorn's lemma, every nonpermutative variety contains an almost permutative variety as a subvariety. We describe almost permutative varieties of algebras over a finite field and almost commutative varieties of rings. In [Algebra Logika, 51, No. 6, 783–804 (2012)], such varieties were characterized for the case of algebras over an infinite field.

Keywords: varieties of associative algebras, PI-algebras, permutation identity, almost commutative (permutative) varieties.

Full text: PDF file (339 kB)
References: PDF file   HTML file

English version:
Algebra and Logic, 2014, 52:6, 484–510

Bibliographic databases:

UDC: 512.552.4
Received: 31.07.2013
Revised: 24.09.2013

Citation: O. B. Finogenova, “Almost commutative varieties of associative rings and algebras over a finite field”, Algebra Logika, 52:6 (2013), 731–768; Algebra and Logic, 52:6 (2014), 484–510

Citation in format AMSBIB
\Bibitem{Fin13}
\by O.~B.~Finogenova
\paper Almost commutative varieties of associative rings and algebras over a~finite field
\jour Algebra Logika
\yr 2013
\vol 52
\issue 6
\pages 731--768
\mathnet{http://mi.mathnet.ru/al616}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3242619}
\transl
\jour Algebra and Logic
\yr 2014
\vol 52
\issue 6
\pages 484--510
\crossref{https://doi.org/10.1007/s10469-014-9262-0}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000332578600005}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84897630318}


Linking options:
  • http://mi.mathnet.ru/eng/al616
  • http://mi.mathnet.ru/eng/al/v52/i6/p731

    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. O. B. Finogenova, “Pochti lievo nilpotentnye mnogoobraziya assotsiativnykh kolets”, Sib. elektron. matem. izv., 12 (2015), 901–909  mathnet  crossref
    2. A. V. Kislitsin, “On nonnilpotent almost commutative $L$-varieties of vector spaces”, Siberian Math. J., 59:3 (2018), 458–462  mathnet  crossref  crossref  isi  elib
  • Алгебра и логика Algebra and Logic
    Number of views:
    This page:168
    Full text:48
    References:38
    First page:15

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021