(untitled) (European Journal of Pure and Applied Mathematics, 2026)
We introduce and study the notion of T-closed dual Rickart modules, which generalizes that of closed dual Rickart modules. A right R-module M is called T-closed dual Rickart if for every endomorphism f of M, the image im(f) is a T-closed submodule of M, where T is a fixed submodule of M. We establish fundamental properties of this class, including its behavior under direct summands, direct sums, and homomorphic images. Characterizations in terms of the endomorphism ring and several equivalent conditions are provided. We also explore connections with well-known classes of modules such as coquasi-Dedekind, continuous, and quasi-continuous modules. Examples are provided to illustrate and delimit the theory.