On (n, d)-Krull Rings

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 Words:

• Krull dimension
• n-presentation
• Trivial extension
• Projective Dimension
• (n, d)-properties, (n, d)-Krull properties

Acknowledgments