Comparability, Stability, and Completions of Ideals

Abstract

In this paper, we study the properties of 1-comparability and stable range one condition on ideals of regular rings, and we use these results to investigate normalized pseudo-rank functions on ideals and N*-complete ideals. These will generalize the corresponding results of Goodearl. Finally, we give some sufficient conditions under which ℙ(I) is compact.

Key Words:

• Regular ring
• 1-Comparability
• N*-Complete ideal
• Compact space

2000 Mathematics Subject Classification:

• 16E50
• 16E20

Acknowledgments

The authors would like to thank the referee for his/her excellent suggestions and corrections which helped us improve considerably the first version of the paper. This work is supported by the National Science Foundation of China (No: 10071035).

Notes

^#Communicated by B. Huisgen-Zimmermann.