Notes on influence of λt-isotype submodules on QTAG-modules

The determination of the QTAG-modules in which every submodule is isotype is a relatively routine exercise. There are many ideas of this type; for instance, the determination of the QTAG-modules in which every h-pure submodule is isotype due to Hasan et al. (Contrib. Math., 2023) and the QTAG-modules in which every λt-isotype submodule is isotype due to Hasan et al. (Gulf J. Math., 2025). The objective of this article is to explore in this direction some new characterizations by determining the QTAG-modules in which every submodule is a center of λt-isotypity and the QTAG-modules in which every λt-isotype submodule is μt-isotype.