Classes of Commutative Rings Defined by Special Conditions |
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Authors: | N Mahdou |
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Institution: | 1. Département de Mathématiques et Informatique , FST Fès-Sa?ss, Université de Fès , Fès, Morocco mahdou@hotmail.com |
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Abstract: | ABSTRACT In this article, we are mainly concerned with (n, d)-Krull rings, i.e., rings in which each n-presented prime ideal has height at most d. Precisely, we show that weakly n-Von Neumann regular rings are (n ? 1, 0)-Krull rings. Also, we prove that (n, d)-Krull property is not local property and that R is an (n, d)-Krull ring if and only if dim(R P ) ≤ d for each n-presented prime ideal P of R. Finally, we construct a class of (2, d)-Krull rings which are neither (2, d ? 1)-Krull rings (for d = 1) nor (1, d)-Krull rings for d = 0,1. |
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Keywords: | n-presentation (n d)-Krull ring Trivial extension Weak n-Von Neumann regular ring |
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