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Algebra Discrete Math., 2012, Volume 13, Issue 2, Pages 273–288 (Mi adm77)  

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

RESEARCH ARTICLE

On inverse operations in the lattices of submodules

A. I. Kashu

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

Abstract: In the lattice ${\boldsymbol{L}}(_RM)$ of submodules of an arbitrary left $R$-module $ _RM$ four operation were introduced and investigated in the paper [3]. In the present work the approximations of inverse operations for two of these operations (for $\alpha$-product and $\omega$-coproduct) are defined and studied. Some properties of left quotient with respect to $\alpha$-product and right quotient with respect to $\omega$-coproduct are shown, as well as their relations with the lattice operations in ${\boldsymbol{L}}(_RM)$ (sum and intersection of submodules). The particular case $ _RM= _RR$ of the lattice ${\boldsymbol{L}}(_RR)$ of left ideals of the ring $R$ is specified.

Keywords: ring, module, preradical, lattice, $\alpha$-product of submodules, left (right) quotient.

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Bibliographic databases:

Document Type: Article
MSC: 16D90, 16S90, 06B23
Received: 22.02.2012
Accepted:22.02.2012
Language: English

Citation: A. I. Kashu, “On inverse operations in the lattices of submodules”, Algebra Discrete Math., 13:2 (2012), 273–288

Citation in format AMSBIB
\Bibitem{Kas12}
\by A.~I.~Kashu
\paper On inverse operations in the lattices of submodules
\jour Algebra Discrete Math.
\yr 2012
\vol 13
\issue 2
\pages 273--288
\mathnet{http://mi.mathnet.ru/adm77}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3027510}
\zmath{https://zbmath.org/?q=an:1258.16012}


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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, “A survey of results on radicals and torsions in modules”, Algebra Discrete Math., 21:1 (2016), 69–110  mathnet  mathscinet
    3. 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
    4. 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
  • Algebra and Discrete Mathematics
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