ieja

International Electronic Journal of Algebra

1306-6048

Abdullah HARMANCI

ON PRINCIPALLY LIFTING MODULES

Kamal

Mahmoud A.

Yousef

Ahmed

12 01 2007

2 2 127 137 12 01 2007

2007

International Electronic Journal of Algebra

Discrete (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 (D1). Here we focus on and study principally lifting modules, or modules with the condition (PD1). These modules are generalizations of lifting modules. We also study direct sums of P-hollow (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 (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 (PD1) are direct sums of P-hollow (semi-hollow) submodules. We also obtain some properties for modules with (PD1), which are in analogy with the known properties for lifting modules.

Projective modules discrete modules

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Mahmoud A. Kamal * and Ahmed Yousef

Faculty of Education, Ain Shams Univ., Roxy, Cairo, Egypt.

E-mail: * mahmoudkamal333@hotmail.com