This article is cited in 9 papers

RESEARCH ARTICLE

Closure operators in the categories of modules. Part I (Weakly hereditary and idempotent operators)

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 the closure operators of a category of modules $R$-Mod are studied. Every closure operator $C$ of $R$-Mod defines two functions $\mathcal{F}_1^{C}$ and $\mathcal{F}_2^{C}$, which in every module $M$ distinguish the set of $C$-dense submodules $\mathcal{F}_1^{C}(M)$ and the set of $C$-closed submodules $\mathcal{F}_2^{C}(M)$. By means of these functions three types of closure operators are described: 1) weakly hereditary; 2) idempotent; 3) weakly hereditary and idempotent.

Keywords: ring, module, lattice, preradical, closure operator, lattice of submodules, dense submodule, closed submodule.

MSC: 16D90, 16S90, 06B23

Received: 19.02.2013
Revised: 25.05.2013

Language: English

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