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IMI/Publicaţii/BASM/Ediţii/BASM n.1(83), 2017/

On the inverse operations in the class of preradicals of a module category, I

Authors: Ion Jardan

Abstract

In the class $\,\mathbb P \mathbb R\,$ of preradicals of the category of left $R$-modules $R$-Mod a new operation is defined and studied, namely the left quotient with respect to join. Some properties of this operation are shown, its compatibility with the lattice operations of $\,\mathbb P \mathbb R\,$ (meet and join of preradicals), as well as the relations with some constructions in the "big" lattice $\,\mathbb P \mathbb R\,$. Also some particular cases are examined.

Technical University of Moldova
Institute of Mathematics and Computer Science
Academy of Sciences of Moldova
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