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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Algebra Discrete Math.:
Year:
Volume:
Issue:
Page:
Find






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


Algebra Discrete Math., 2010, Volume 9, Issue 2, Pages 127–139 (Mi adm34)  

RESEARCH ARTICLE

Biserial minor degenerations of matrix algebras over a field

Anna Włodarska

Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, 87-100 Toruń, Poland

Abstract: Let $n\geq 2$ be a positive integer, $K$ an arbitrary field, and $q=[q^{(1)}|…|q^{(n)}]$ an $n$-block matrix of $n\times n$ square matrices $q^{(1)},…,q^{(n)}$ with coefficients in $K$ satisfying the conditions (C1) and (C2) listed in the introduction. We study minor degenerations $\mathbb M^q_n(K)$ of the full matrix algebra $\mathbb M_n(K)$ in the sense of Fujita–Saka—Simson [7]. A characterisation of all block matrices $q=[q^{(1)}|…|q^{(n)}]$ such that the algebra $\mathbb M^q_n(K)$ is basic and right biserial is given in the paper. We also prove that a basic algebra $\mathbb M^q_n(K)$ is right biserial if and only if $\mathbb M^q_n(K)$ is right special biserial. It is also shown that the $K$-dimensions of the left socle of $\mathbb M^q_n(K)$ and of the right socle of $\mathbb M^q_n(K)$ coincide, in case $\mathbb M^q_n(K)$ is basic and biserial.

Keywords: right special biserial algebra, biserial algebra, Gabriel quiver.

Full text: PDF file (262 kB)

Bibliographic databases:
MSC: 16G10, 16G60, 14R20, 16S80
Received: 09.03.2010
Revised: 14.10.2010
Language:

Citation: Anna Włodarska, “Biserial minor degenerations of matrix algebras over a field”, Algebra Discrete Math., 9:2 (2010), 127–139

Citation in format AMSBIB
\Bibitem{Wlo10}
\by Anna W{\l}odarska
\paper Biserial minor degenerations of matrix algebras over a~field
\jour Algebra Discrete Math.
\yr 2010
\vol 9
\issue 2
\pages 127--139
\mathnet{http://mi.mathnet.ru/adm34}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2808786}
\zmath{https://zbmath.org/?q=an:1209.16021}


Linking options:
  • http://mi.mathnet.ru/eng/adm34
  • http://mi.mathnet.ru/eng/adm/v9/i2/p127

    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
  • Algebra and Discrete Mathematics
    Number of views:
    This page:139
    Full text:50
    First page:1

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