<i>w</i> -locally isomorphic torsionless modules over weakly Matlis domains (Q6594872)

In this paper, the authors introduce two novel concepts, \(w\)-local isomorphism and \(w\)-nearly isomorphism, for torsionless modules over weakly Matlis domains, expanding the framework of \(w\)-operations in module theory. They establish the equivalence and implications between \(w\)-local isomorphism, \(w\)-nearly isomorphism, and stable isomorphism under various structural assumptions. Additionally, they provide new insights into the decomposition and characterization of torsionless \(w\)-modules over weakly Matlis domains, offering a deeper understanding of their behavior and classification. Several illustrative examples are included to highlight the necessity of the assumptions in their main results.