ON PRINCIPALLY LIFTING MODULES

Authors : Mahmoud A KAMAL, Ahmed Yousef

Pages : 127-137

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Publication Date : 2007-12-01

Article Type : Research Paper

Abstract :Discrete insert ignore into journalissuearticles values(quasi-discrete); modules form an important class in module theory, they are studied extensively by many authors. The class of lifting modules is obtained by considering only one of the defining conditions of quasi-discrete modules, namely the condition insert ignore into journalissuearticles values(D1);. Here we focus on and study principally lifting modules, or modules with the condition insert ignore into journalissuearticles values(PD1);. These modules are generalizations of lifting modules. We also study direct sums of P-hollow insert ignore into journalissuearticles values(semi-hollow); modules. It is known that relative projectivity is essential to study direct sums of quasi-discrete modules. Here we introduce the definition of relative Pprojectivity, which is essential to examine direct sums of hollow, and of P-hollow insert ignore into journalissuearticles values(semi hollow);, modules for being principally lifting. Quasi-discrete module are always direct sums of hollow submodules, we show that finite dimensional modules with the condition insert ignore into journalissuearticles values(PD1); are direct sums of P-hollow insert ignore into journalissuearticles values(semi-hollow); submodules. We also obtain some properties for modules with insert ignore into journalissuearticles values(PD1);, which are in analogy with the known properties for lifting modules.
Keywords : Projective modules, discrete modules