On questions related to normal pairs

Abstract

In this current paper, we identify some new properties concerning normal pairs (R, S). Among other interesting results, we show that every prime ideal P of R that is the radical of a finitely generated ideal A such that AS = S is the radical of an ideal with a basis of two elements. Consequently, we derive a significant improvement of Pendleton’s Criterion by producing further characterizations of QR-pairs.

Keywords:

• Invertible ideal
• Noetherian domain
• normal pair
• QR-pair
• residually algebraic pair

2010 Mathematics Subject Classification:

• primary 13B02
• secondary 13A18
• 13A35
• 13B25
• 13B35
• 13E05

Acknowledgements

We would like to thank the anonymous reviewer for his/her comments and suggestions concerning the final form of this paper.