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



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






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


Vladikavkaz. Mat. Zh., 2007, Volume 9, Number 2, Pages 3–8 (Mi vmj90)  

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

On a decomposition equality in modular group rings

P. V. Danchev

Plovdiv State University Paissii Hilendarski, Plovdiv, Bulgaria

Abstract: Let $G$ be an abelian group such that $A\le G$ with $p$-component $A_p$ and $B\le G$, and let $R$ be a commutative ring with 1 of prime characteristic $p$ with nil-radical $N(R)$. It is proved that if $A_p\not\subseteq B_p$ or $N(R)\ne 0$, then $S(RG)=S(RA)(1+I_p(RG;B))$ $\iff$ $G=AB$ and $G_p=A_pB_p$. In particular, if $A_p\ne 1$ or $N(R)\ne 0$, then $S(RG)=S(RA)\times (1+I_p(RG;B))$ $\iff$ $G=A\times B$. So, the question concerning the validity of this formula is completely exhausted. The main statement encompasses both the results of this type established by the author in (Hokkaido Math. J., 2000) and (Miskolc Math. Notes, 2005). We also point out and eliminate in a concrete situation an error in the proof of a statement due to T. Zh. Mollov on a decomposition formula in commutative modular group rings (Proceedings of the Plovdiv University-Math., 1973).

Key words: direct factors, decompositions, normed unit groups, homomorphisms.

Full text: PDF file (131 kB)
References: PDF file   HTML file

Bibliographic databases:
UDC: 512.742
MSC: 16S34, 16U60, 20K10, 20K21
Received: 03.07.2006
Language:

Citation: P. V. Danchev, “On a decomposition equality in modular group rings”, Vladikavkaz. Mat. Zh., 9:2 (2007), 3–8

Citation in format AMSBIB
\Bibitem{Dan07}
\by P.~V.~Danchev
\paper On a decomposition equality in modular group rings
\jour Vladikavkaz. Mat. Zh.
\yr 2007
\vol 9
\issue 2
\pages 3--8
\mathnet{http://mi.mathnet.ru/vmj90}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2434626}


Linking options:
  • http://mi.mathnet.ru/eng/vmj90
  • http://mi.mathnet.ru/eng/vmj/v9/i2/p3

    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. P. V. Danchev, “A note on decompositions in abelian group rings”, An. Ştiinţ. Univ. “Ovidius” Constanţa Ser. Mat., 16:1 (2008), 73–76  mathscinet  zmath  isi
  • Number of views:
    This page:132
    Full text:95
    References:30
    First page:1

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