w-locally isomorphic torsionless modules over weakly Matlis domains

Abstract

Let R be an integral domain. An R-module G is torsionless if it is isomorphic to a submodule of a finitely generated free R-module. For torsionless modules, we define w-weak isomorphism types which are new versions of weak isomorphism types with respect to the w-operation: w-local isomorphism and w-nearly isomorphism. Furthermore, we examine the relationship between w-local isomorphism, w-nearly isomorphism, and stable isomorphism for torsionless w-modules over weakly Matlis domains.

KEYWORDS:

• The w-operation
• torsion-free modules
• weakly Matlis domain

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 13A15
• 13F05
• Secondary: 13C05
• 20K15

Acknowledgments

The authors would like to thank the referee for his/her helpful comments and suggestions.

Additional information

Funding

Haleh Hamdi was supported by a research grant of Türkiye Scholarships (21IR022538) funded by Presidency For Turks Abroad And Related Communities.