A CLASS OF RINGS FOR WHICH THE LATTICE OF PRERADICALS IS NOT A SET

Year 2011, Volume: 9 Issue: 9 , 38 - 60 , 01.06.2011

Rogelio Fernández-alonso Silvia Gavito Henry Chimal-dzul

https://izlik.org/JA45LD34ZU

Abstract

In this paper we define Z-coinitial rings, where Z is an integral
domain, and prove some of their properties. In particular, we characterize
commutative noetherian domains and discrete valuation domains which are
Z-coinital. We define radical modules and radical rings, and we prove that
every countable Z-coinitial and right hereditary ring is a right radical ring.
We give some examples of rings satisfying these conditions. Finally, we prove
that the lattice of preradicals of every right radical ring is not a set.

Keywords

preradical , Z-coinitial ring , radical ring , hereditary ring , Dedekind domain