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.
preradical Z-coinitial ring radical ring hereditary ring Dedekind domain
Diğer ID | JA85DU28SS |
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Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 1 Haziran 2011 |
Yayımlandığı Sayı | Yıl 2011 Cilt: 9 Sayı: 9 |