GENERALIZED COFINITELY SEMIPERFECT MODULES
In the present paper, we define generalized (amply) cofinitely supplemented modules, and generalized ⊕-cofinitely supplemented modules are defined as a generalization of (amply) cofinitely supplemented modules and ⊕-cofinitely supplemented modules, respectively, and show, among others, the following results: (1) The class of generalized cofinitely supplemented modules is closed under taking homomorphic images, generalized covers and arbitrary direct sums. (2) Any finite direct sum of generalized ⊕-cofinitely supplemented modules is a generalized ⊕-cofinitely supplemented module. (3) M is a generalized cofinitely semiperfect module if and only if M is a generalized cofinitely supplemented -module by supplements which have generalized projective covers.
Keywords:
Cofinite submodule, generalized supplement submodule, generalized projective cover semiperfect module,
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- Department of Mathematics, Faculty of Science, Gebze Institute of Technology C¸ ayırova Campus 41400 Gebze-Kocaeli, Turkey email: mtkosan@gyte.edu.tr
- ISSN: 1306-6048
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2007
- Yayıncı: Abdullah HARMANCI