This article is cited in 8 papers

RESEARCH ARTICLE

Closure operators in the categories of modules. Part II (Hereditary and cohereditary operators)

A. I. Kashu

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

Abstract: This work is a continuation of the paper [1] (Part I), in which the weakly hereditary and idempotent closure operators of the category $R$-Mod are described. Using the results of [1], in this part the other classes of closure operators $C$ are characterized by the associated functions $\mathcal{F}_1^{C}$ and $\mathcal{F}_2^{C}$ which separate in every module $M \in R$-Mod the sets of $C$-dense submodules and $C$-closed submodules. This method is applied to the classes of hereditary, maximal, minimal and cohereditary closure operators.

Keywords: ring, module, preradical, closure operator, dense submodule, closed submodule, hereditary (cohereditary) closure operator.

MSC: 16D90, 16S90, 06B23

Received: 03.06.2013
Revised: 03.06.2013

Language: English

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