This article is cited in 3 papers

RESEARCH ARTICLE

Preradicals, closure operators in $R$-Mod and connection between them

A. I. Kashu

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

Abstract: For a module category $R$-Mod the class $\mathbb{PR}$ of preradicals and the class $\mathbb{CO}$ of closure operators are studied. The relations between these classes are realized by three mappings: $\Phi : \mathbb{CO} \to \mathbb{PR}$ and $\Psi_1, \Psi_2 : \mathbb{PR} \to \mathbb{CO}$. The impact of these mappings on the operations in $\mathbb{PR}$ and $\mathbb{CO}$ (meet, join, product, coproduct) is investigated. It is established that in most cases the considered mappings preserve the lattice operations (meet and join), while the other two operations are converted one into another (i.e. the product into the coproduct and vice versa).

Keywords: ring, module, lattice, preradical, closure operator, product (coproduct) of closure operators.

MSC: 16D90, 16S90, 06B23

Received: 09.07.2014
Revised: 09.07.2014

Language: English

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