
This article is cited in 4 scientific papers (total in 4 papers)
RESEARCH ARTICLE
Preradicals and characteristic submodules: connections and operations
A. I. Kashu^{} ^{} Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, 5 Academiei str. Chişinău, MD2028 Moldova
Abstract:
For an arbitrary module $M\in R$Mod the relation between the lattice $L^{ch}(_{R}M)$ of characteristic (fully invariant) submodules of $M$ and big lattice $R$pr of preradicals of $R$Mod is studied. Some isomorphic images of $L^{ch}(_{R}M)$ in $R$pr are constructed. Using the product and coproduct in $R$pr four operations in the lattice $L^{ch}(_{R}M)$ are defined. Some properties of these operations are shown and their relations with the lattice operations in $L^{ch}(_{R}M)$ are investigated. As application the case $_{R}M=_{R}R$ is mentioned, when $L^{ch}(_{R}R)$ is the lattice of twosided ideals of ring $R$.
Keywords:
preradical, lattice, characteristic submodule, product (coproduct) of preradicals.
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MSC: 16D90, 16S90, 06B23 Received: 22.04.2010 Revised: 11.08.2010
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Citation:
A. I. Kashu, “Preradicals and characteristic submodules: connections and operations”, Algebra Discrete Math., 9:2 (2010), 61–77
Citation in format AMSBIB
\Bibitem{Kas10}
\by A.~I.~Kashu
\paper Preradicals and characteristic submodules: connections and operations
\jour Algebra Discrete Math.
\yr 2010
\vol 9
\issue 2
\pages 6177
\mathnet{http://mi.mathnet.ru/adm29}
\mathscinet{http://www.ams.org/mathscinetgetitem?mr=2808781}
\zmath{https://zbmath.org/?q=an:1208.16014}
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http://mi.mathnet.ru/eng/adm29 http://mi.mathnet.ru/eng/adm/v9/i2/p61
Citing articles on Google Scholar:
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Russian articles,
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This publication is cited in the following articles:

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

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

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

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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