This article is cited in 4 papers

Research articles

On natural classes of $R$-modules in the language of ring $R$

A. I. Kashu

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chişinău, Moldova

Abstract: Every natural class of left $R$-modules is closed, i.e. is completely described by special set of left ideals of $R$ (natural set). Some characterizations of such sets are shown. The complementation operator of sets is defined and its properties permit to transfer some results on natural classes to the lattice of left ideals of $R$.

Keywords and phrases: Natural class, closed class, natural set, boolean lattice, filter.

MSC: 16S90, 16D90, 16D80

Received: 28.09.2004

Language: English

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