ON PRINCIPALLY LIFTING MODULES
ON PRINCIPALLY LIFTING MODULES
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.
Keywords:
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
- ISSN: 1306-6048
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2007
- Yayıncı: Abdullah HARMANCI
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