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 Bul. Acad. Ştiinţe Repub. Mold. Mat.: Year: Volume: Issue: Page: Find

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

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:
MSC: 16D90, 16S90, 06B23
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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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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
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