Semiprime Preradicals

Abstract

We define the concept of “semiprime” for preradicals and for submodules, and we prove some properties that relate both of them. Related concepts are defined in article by Bican et al. [2] and by Van den Berg and Wisbauer [9]. For any ring, we compare the least semiprime preradical, the Jacobson radical and the join of all nilpotent preradicals, and we characterize V-rings in terms of these three preradicals. We study the least semiprime preradical above any preradical and we prove some of its properties. Using “Amitsur constructions” we define another related operators and prove some of their properties.

Key Words:

• Lattice
• Operator
• Preradical
• Semiprime

2000 Mathematics Subject Classification:

• Primary 16N99, 16S99
• Secondary 06C05, 16N20

ACKNOWLEDGMENT

The authors wish to thank the referee for all the suggestions and comments.

Notes

Communicated by R. Wisbauer.