Module theory is an important tool for many different branches of mathematics, as well as
being an interesting subject in its own right. Within module theory, the concept of injective …

Extending modules are generalizations of injective modules and, dually, lifting modules
generalize projective supplemented modules. There is a certain asymmetry in this duality …

Let R be a ring with identity and let be a finite direct sum of relatively protective R-modules
Mi Then it is proved that M is lifting if and only if M is amply supplemented and Mi is lifting for …

This dissertation reviews attempts of dualizing the Goldie dimension. Moreover we choose
one of these attempts as the dualization of Goldie dimension and study modules with this …

ABSTRACT PF Smith studied modules in which every submodule has a unique closure and
called them UC modules. In this paper we consider modules with the dual property viz …

Let $ R $ be any ring and let $ M $ be any right $ R $-module. $ M $ is called hollow-lifting if
every submodule $ N $ of $ M $ such that $ M/N $ is hollow has a coessential submodule …

Recently, in [2], Harada and Tozaki defined'almost M-projectives* which are generalized
from the concept'M-projectives' due to Azumaya. In this paper we shall define a dual …

It was shown in Dung-Smith [2] that, for a module M, every module in σ [M] is extending (CS
module) if and only if every module in σ [M] is a direct sum of indecomposable modules of …

Harada (cf.) introduced the lifting property for maximal submodules and the extending
property for simple submodules, and Oshiro (cf.) definitely introduced lifting modules and …

This paper is supplemental to [4],[6] and [7]. We shall show, under assumption of finite
length, that when we study almost relative projectives, we may restrict ourselves only to …