Akademik Veri Yönetim Sistemi
International Conference on Rings and Things held in Honor of Carl Faith and Barbara Osofsky, Ohio, Amerika Birleşik Devletleri, 15 - 17 Haziran 2007, cilt.480, ss.133-137, (Tam Metin Bildiri)
In a recent paper Carl Faith introduced the right CSI rings, namely, rings over which injective hulls of cyclic right modules are Sigma-injective. It is not known whether a right CSI ring is right Noetherian. Faith gave an affirmative answer to this question for several types of rings such as semilocal, commutative, right continuous, right Kasch rings as well as rings every sub-factor of which contains its radical properly. In this paper, characterizations of Noetherian rings are given in terms of the CSI and the q.f.d. conditions. Also it is shown that, over a right CSI ring R, all finitely generated right modules are Hopfian. This implies, by a result of Coodearl, that M-n(R) is right repetitive for all n is an element of N.