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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2012, Number 2, Pages 59–73 (Mi basm316)  

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

On partial inverse operations in the lattice of submodules

A. I. Kashu

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

Abstract: In the present work two partial operations in the lattice of submodules $\boldsymbol L(_RM)$ are defined and investigated. They are the inverse operations for $\omega$-product and $\alpha$-coproduct studied in [6]. This is the continuation of the article [7], in which the similar questions for the operations of $\alpha$-product and $\omega$-coproduct are investigated.
The partial inverse operation of left quotient $N /_\odot K$ of $N$ by $K$ with respect to $\omega$-product is introduced and similarly the right quotient $N _:\backslash K$ of $K$ by $N$ with respect to $\alpha$-coproduct is defined, where $N,K\in\boldsymbol L(_RM)$. The criteria of existence of such quotients are indicated, as well as the different forms of representation, the main properties, the relations with lattice operations in $\boldsymbol L(_RM)$, the conditions of cancellation and other related questions are elucidated.

Keywords and phrases: ring, module, lattice, preradical, (co)product of preradical, left (right) quotient of submodules.

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Bibliographic databases:

Document Type: Article
MSC: 16D90, 16S90, 06B23
Received: 15.05.2012
Language: English

Citation: A. I. Kashu, “On partial inverse operations in the lattice of submodules”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2012, no. 2, 59–73

Citation in format AMSBIB
\Bibitem{Kas12}
\by A.~I.~Kashu
\paper On partial inverse operations in the lattice of submodules
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2012
\issue 2
\pages 59--73
\mathnet{http://mi.mathnet.ru/basm316}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3060802}
\zmath{https://zbmath.org/?q=an:06179496}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. I. Kashu, “A survey of results on radicals and torsions in modules”, Algebra Discrete Math., 21:1 (2016), 69–110  mathnet  mathscinet
  • Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
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