Affiliation:
1. Faculty of Mathematics and Computer and Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran
Abstract
In this paper, we introduce a class of commutative rings which is a generalization of ZD-rings and rings with Noetherian spectrum. A ring [Formula: see text] is called strongly[Formula: see text]-Noetherian whenever the ring [Formula: see text] is [Formula: see text]-Noetherian for every non-nilpotent [Formula: see text]. We give some characterizations for strongly [Formula: see text]-Noetherian rings and, among the other results, we show that if [Formula: see text] is strongly [Formula: see text]-Noetherian, then [Formula: see text] has Noetherian spectrum, which is a generalization of Theorem 2 in Gilmer and Heinzer [The Laskerian property, power series rings, and Noetherian spectra, Proc. Amer. Math. Soc. 79 (1980) 13–16].
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory