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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2011, Number 2, Pages 5–16 (Mi basm284)  

This article is cited in 5 scientific papers (total in 5 papers)

On some operations in the lattice of submodules determined by preradicals

A. I. Kashu

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chişinău, Moldova

Abstract: In the lattice $\boldsymbol L(_RM)$ of all submodules of a module $_RM$ four operations are defined using the standard preradicals: $\alpha$-product, $\omega$-product, $\alpha$-coproduct and $\omega$-coproduct. Some properties of these operations, as well as some connections with the lattice operations of $\boldsymbol L(_RM)$ are indicated. For characteristic submodules these operations were studied in the work [5].

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

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Document Type: Article
MSC: 16D90, 16S90, 06B23
Received: 20.03.2011
Language: English

Citation: 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

Citation in format AMSBIB
\Bibitem{Kas11}
\by A.~I.~Kashu
\paper On some operations in the lattice of submodules determined by preradicals
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2011
\issue 2
\pages 5--16
\mathnet{http://mi.mathnet.ru/basm284}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2895773}
\zmath{https://zbmath.org/?q=an:1248.16006}


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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 partial inverse operations in the lattice of submodules”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2012, no. 2, 59–73  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, “A survey of results on radicals and torsions in modules”, Algebra Discrete Math., 21:1 (2016), 69–110  mathnet  mathscinet
    4. Ion Jardan, “On the inverse operations in the class of preradicals of a module category, I”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2017, no. 1, 57–66  mathnet  mathscinet
    5. Ion Jardan, “On the inverse operations in the class of preradicals of a module category, II”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2017, no. 2, 77–87  mathnet  mathscinet
  • Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
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