Characterizations of generalized submodules of QTAG-modules

Abstract

. We characterize the α -large submodules of α -modules in terms of certain sequences of ordinals, and give some of their interesting properties. Also, we deal with α -large submodules of the closure of an unbounded direct sum of uniserial modules, and the α -large submodules of the smallest α -pure fully invariant submodules of the closure containing a given element.