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- W2023117408 abstract "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." @default.
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- W2023117408 date "2003-01-05" @default.
- W2023117408 modified "2023-09-30" @default.
- W2023117408 title "On Nonnil-Noetherian Rings" @default.
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- W2023117408 doi "https://doi.org/10.1081/agb-120018502" @default.
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