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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2014, Number 3, Pages 13–22
(Mi basm375)
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This article is cited in 3 scientific papers (total in 3 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.
Received: 03.03.2014
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
Linking options:
https://www.mathnet.ru/eng/basm375 https://www.mathnet.ru/eng/basm/y2014/i3/p13
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Abstract page: | 227 | Full-text PDF : | 55 | References: | 42 |
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