GENERALIZED COFINITELY SEMIPERFECT MODULES

Yıl 2009, Cilt: 5 Sayı: 5, 58 - 69, 01.06.2009

M. Tamer Koşan

Öz

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.

Anahtar Kelimeler

Cofinite submodule, generalized supplement submodule, generalized projective cover, semiperfect module

Kaynakça

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• Department of Mathematics, Faculty of Science, Gebze Institute of Technology C¸ ayırova Campus 41400 Gebze-Kocaeli, Turkey email: [e-mail]