The Lattice Structure of Preradicals

In this paper we study the lattice of all preradicals on a ring R. We describe this lattice, we prove that it is an atomic and coatomic lattice and we describe the atoms and coatoms. We also give characterizations of simple Artinian, semisimple Artinian, and V-rings in terms of preradicals.

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Bibliographic Details
Published in:Communications in algebra 2002-01, Vol.30 (3), p.1533-1544
Main Authors: Raggi, Francisco, Montes, José Ríos, Rincón, Hugo, Fernández-Alonso, Rogelio, Signoret, Carlos
Format: Article
Language:English
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Description
Summary:In this paper we study the lattice of all preradicals on a ring R. We describe this lattice, we prove that it is an atomic and coatomic lattice and we describe the atoms and coatoms. We also give characterizations of simple Artinian, semisimple Artinian, and V-rings in terms of preradicals.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927870209342395