ScholarLens Back to search
2003•Communications in AlgebraRequires access

On ( n , d )-Krull Rings

Najib Mahdou

Open publisher page 2 citations

Abstract

In this paper, we introduce the notion of “(n, d)-Krull rings” which is in some way a generalization of the notion of “Krull dimension rings”. The richness of this notion resides in its ability to classify some rings having infinite Krull dimension. We establish the transfer of this notion to the trivial extension and to the direct product notions. We conclude with a brief discussion of the scopes and limits of our results.

About this research paper

What this paper is about

In this paper, we introduce the notion of “(n, d)-Krull rings” which is in some way a generalization of the notion of “Krull dimension rings”. The richness of this notion resides in its ability to classify some rings having infinite Krull dimension. We establish the transfer of this notion to the trivial extension and to the direct product notions. We conclude with a brief discussion of the scopes and limits of our results.

Why it matters

OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

In this paper, we introduce the notion of “(n, d)-Krull rings” which is in some way a generalization of the notion of “Krull dimension rings”. The richness of this notion resides in its ability to classify some rings having infinite Krull dimension. We establish the transfer of this notion to the trivial extension and to the direct product notions. We conclude with a brief discussion of the scopes and limits of our results.

Key concepts: Krull dimension, Mathematics, Generalization, Regular local ring, Global dimension, Dimension theory (algebra), Pure mathematics, Dimension (graph theory)

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
On ( n , d )-Krull Rings — Research Paper | ScholarLens