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

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International Electronic Journal of Algebra
Volume:9 Issue:9
A CLASS OF RINGS FOR WHICH THE LATTICE OF PRERADICALS IS NOT A SET

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

Authors : Rogelio FernándezAlonso, Silvia Gavito, Henry ChimalDzul

Pages : 38-60

View : 13 | Download : 8

Publication Date : 2011-06-01

Article Type : Research Paper

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

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