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Algebra Discrete Math., 2010, Volume 9, Issue 2, Pages 61–77 (Mi adm29)  

This article is cited in 4 scientific papers (total in 4 papers)

RESEARCH ARTICLE

Preradicals and characteristic submodules: connections and operations

A. I. Kashu

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

Abstract: For an arbitrary module $M\in R$-Mod the relation between the lattice $L^{ch}(_{R}M)$ of characteristic (fully invariant) submodules of $M$ and big lattice $R$-pr of preradicals of $R$-Mod is studied. Some isomorphic images of $L^{ch}(_{R}M)$ in $R$-pr are constructed. Using the product and coproduct in $R$-pr four operations in the lattice $L^{ch}(_{R}M)$ are defined. Some properties of these operations are shown and their relations with the lattice operations in $L^{ch}(_{R}M)$ are investigated. As application the case $_{R}M=_{R}R$ is mentioned, when $L^{ch}(_{R}R)$ is the lattice of two-sided ideals of ring $R$.

Keywords: preradical, lattice, characteristic submodule, product (coproduct) of preradicals.

Full text: PDF file (292 kB)

Bibliographic databases:
MSC: 16D90, 16S90, 06B23
Received: 22.04.2010
Revised: 11.08.2010
Language:

Citation: A. I. Kashu, “Preradicals and characteristic submodules: connections and operations”, Algebra Discrete Math., 9:2 (2010), 61–77

Citation in format AMSBIB
\Bibitem{Kas10}
\by A.~I.~Kashu
\paper Preradicals and characteristic submodules: connections and operations
\jour Algebra Discrete Math.
\yr 2010
\vol 9
\issue 2
\pages 61--77
\mathnet{http://mi.mathnet.ru/adm29}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2808781}
\zmath{https://zbmath.org/?q=an:1208.16014}


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    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, “On some operations in the lattice of submodules determined by preradicals”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2011, no. 2, 5–16  mathnet  mathscinet  zmath
    2. A. I. Kashu, “On inverse operations in the lattices of submodules”, Algebra Discrete Math., 13:2 (2012), 273–288  mathnet  mathscinet  zmath
    3. A. I. Kashu, “On partial inverse operations in the lattice of submodules”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2012, no. 2, 59–73  mathnet  mathscinet  zmath
    4. A. I. Kashu, “A survey of results on radicals and torsions in modules”, Algebra Discrete Math., 21:1 (2016), 69–110  mathnet  mathscinet
  • Algebra and Discrete Mathematics
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