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http://hdl.handle.net/20.500.11889/7762
Title: | On Nonnil-Noetherian rings | Authors: | Badawi, Ayman | Keywords: | Noetherian rings;Commutative rings - Chain conditions;Finitely generated ideals;Divided ideals;Phi-rings | Issue Date: | 2003 | Publisher: | Communications in Algebra | Abstract: | Let R be a commutative ring with 1 such that Nil(R) is a divided prime ideal of R. The purpose of this paper is to introduce a new class of rings that is closely related to the class of Noetherian rings. A ring R is called a Nonnil-Noetherian ring if every nonnil ideal of R is finitely generated. We show that many of the properties of Noetherian rings are also true for Nonnil-Noetherian rings; we use the idealization construction to give examples of Nonnil-Noetherian rings that are not Noetherian rings; we show that for each n 1, there is a Nonnil-Noetherian ring with Krull dimension n which is not a Noetherian ring. | URI: | http://hdl.handle.net/20.500.11889/7762 | DOI: | 10.1081/AGB-120018502 |
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