ES-w-stability

Abstract

We introduce and study the notion of ES-w-stability for an integral domain R. A nonzero ideal I of R is called ES-w-stable if ${(I^2)}_w={(JI)}_w$ for some t-invertible ideal J of R contained in I, and I is called weakly ES-w-stable if $I_w={(JE)}_w$ for some t-invertible fractional ideal J of R and w-idempotent fractional ideal E of R. We define R to be an ES-w-stable domain (resp., a weakly ES-w-stable domain) if every nonzero ideal of R is ES-w-stable (resp., weakly ES-w-stable). These notions allow us to generalize some well-known properties of ES-stable and weakly ES-stable domains.

Keywords:

• ES-stable domains
• Krull domains
• weakly ES-stable domains
• w-stable domains

2020 Mathematics Subject Classification:

• Primary: 13G05
• 13A15
• secondary: 13F05
• 13F20

Acknowledgments

The authors would like to thank the referee for his/her careful reading of the manuscript and several comments. The second-named author disclosed receipt of the following financial support for the research.

Additional information

Funding

This research was in part supported by a grant from IPM (No. 991300115).