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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2014, Number 3, Pages 13–22 (Mi basm375)  

This article is cited in 2 scientific papers (total in 2 papers)

Closure operators in the categories of modules. Part IV (Relations between the operators and preradicals)

A. I. Kashu

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

Abstract: In this work (which is a continuation of [1–3]) the relations between the class $\mathbb{CO}$ of the closure operators of a module category $R$-Mod and the class $\mathbb{PR}$ of preradicals of this category are investigated. The transition from $\mathbb{CO}$ to $\mathbb{PR}$ and backwards is defined by three mappings $\Phi\colon \mathbb{CO\to PR}$ and $\Psi_1,\Psi_2\colon\mathbb{CO\to PR}$. The properties of these mappings are studied.
Some monotone bijections are obtained between the preradicals of different types (idempotent, radical, hereditary, cohereditary, etc.) of $\mathbb{PR}$ and the closure operators of $\mathbb{CO}$ with special properties (weakly hereditary, idempotent, hereditary, maximal, minimal, cohereditary, etc.).

Keywords and phrases: ring, module, closure operator, preradical, torsion, radical filter, idempotent ideal.

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Document Type: Article
MSC: 16D90, 16S90, 06B23
Received: 03.03.2014
Language: English

Citation: A. I. Kashu, “Closure operators in the categories of modules. Part IV (Relations between the operators and preradicals)”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2014, no. 3, 13–22

Citation in format AMSBIB
\Bibitem{Kas14}
\by A.~I.~Kashu
\paper Closure operators in the categories of modules. Part~IV (Relations between the operators and preradicals)
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2014
\issue 3
\pages 13--22
\mathnet{http://mi.mathnet.ru/basm375}


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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
    2. A. I. Kashu, “Pretorsions in modules and associated closure operators”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2017, no. 2, 24–41  mathnet  mathscinet
  • Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
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