This article is cited in 6 papers

On some operations in the lattice of submodules determined by preradicals

A. I. Kashu

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

Abstract: In the lattice $\boldsymbol L(_RM)$ of all submodules of a module $_RM$ four operations are defined using the standard preradicals: $\alpha$-product, $\omega$-product, $\alpha$-coproduct and $\omega$-coproduct. Some properties of these operations, as well as some connections with the lattice operations of $\boldsymbol L(_RM)$ are indicated. For characteristic submodules these operations were studied in the work [5].

Keywords and phrases: preradical, lattice, submodule, product (coproduct) of preradicals.

MSC: 16D90, 16S90, 06B23

Received: 20.03.2011

Language: English

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