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

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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MSC: 16D90, 16S90, 06B23
Accepted:22.02.2012
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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
2. A. I. Kashu, “A survey of results on radicals and torsions in modules”, Algebra Discrete Math., 21:1 (2016), 69–110
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
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
5. Jardan I., “on Partial Inverse Operations in the Class of Preradicals of Modules”, Analele Stiint. Univ. Ovidius C., 27:2 (2019), 15–36
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