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., 2014, Volume 18, Issue 1, Pages 86–96 (Mi adm483)  

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

RESEARCH ARTICLE

Preradicals, closure operators in $R$-Mod and connection between them

A. I. Kashu

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, 5 Academiei str., Chişinău, MD – 2028 MOLDOVA

Abstract: For a module category $R$-Mod the class $\mathbb{PR}$ of preradicals and the class $\mathbb{CO}$ of closure operators are studied. The relations between these classes are realized by three mappings: $\Phi : \mathbb{CO} \to \mathbb{PR}$ and $\Psi_1, \Psi_2 : \mathbb{PR} \to \mathbb{CO}$. The impact of these mappings on the operations in $\mathbb{PR}$ and $\mathbb{CO}$ (meet, join, product, coproduct) is investigated. It is established that in most cases the considered mappings preserve the lattice operations (meet and join), while the other two operations are converted one into another (i.e. the product into the coproduct and vice versa).

Keywords: ring, module, lattice, preradical, closure operator, product (coproduct) of closure operators.

Full text: PDF file (316 kB)
References: PDF file   HTML file

Bibliographic databases:
MSC: 16D90, 16S90, 06B23
Received: 09.07.2014
Revised: 09.07.2014
Language:

Citation: A. I. Kashu, “Preradicals, closure operators in $R$-Mod and connection between them”, Algebra Discrete Math., 18:1 (2014), 86–96

Citation in format AMSBIB
\Bibitem{Kas14}
\by A.~I.~Kashu
\paper Preradicals, closure operators in $R$-Mod and connection between them
\jour Algebra Discrete Math.
\yr 2014
\vol 18
\issue 1
\pages 86--96
\mathnet{http://mi.mathnet.ru/adm483}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3280258}


Linking options:
  • http://mi.mathnet.ru/eng/adm483
  • http://mi.mathnet.ru/eng/adm/v18/i1/p86

    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. I. Kashu, “A survey of results on radicals and torsions in modules”, Algebra Discret. Math., 21:1 (2016), 69–110  mathnet  mathscinet  zmath  isi
    2. A. I. Kashu, “Pretorsions in modules and associated closure operators”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2017, no. 2, 24–41  mathnet  mathscinet
  • Algebra and Discrete Mathematics
    Number of views:
    This page:168
    Full text:59
    References:27

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