On λt-isotype submodules of QTAG-modules

Abstract

Let λ = (λ_t)t∈N be an increasing sequence of ordinals. We define the class of λ_t-isotype submodules and study their crucial properties. The paper discusses various contexts in which every λ_t-isotype submodule is an h-neat, an h-pure, an isotype submodule, a direct summand, an absolute direct summand, respectively. Moreover, some comprehensive characterizations in this direction are also established.