w-locally isomorphic torsionless modules over weakly Matlis domains

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-...

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Bibliographic Details
Published in:Communications in algebra 2024-09, Vol.52 (9), p.3721-3733
Main Authors: Ay Saylam, Başak, Gürbüz, Ezgi, Hamdi, Haleh
Format: Article
Language:English
Subjects:
Isomorphism
Modules
Primary: 13A15
Secondary: 13C05
The w-operation
torsion-free modules
weakly Matlis domain
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Summary: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.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2024.2328267