GENERALIZED COFINITELY SEMIPERFECT MODULES

Authors : M Tamer KOŞAN

Pages : 58-69

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Publication Date : 2009-06-01

Article Type : Research Paper

Abstract :In the present paper, we define generalized insert ignore into journalissuearticles values(amply); cofinitely supplemented modules, and generalized ⊕-cofinitely supplemented modules are defined as a generalization of insert ignore into journalissuearticles values(amply); cofinitely supplemented modules and ⊕-cofinitely supplemented modules, respectively, and show, among others, the following results: insert ignore into journalissuearticles values(1); The class of generalized cofinitely supplemented modules is closed under taking homomorphic images, generalized covers and arbitrary direct sums. insert ignore into journalissuearticles values(2); Any finite direct sum of generalized ⊕-cofinitely supplemented modules is a generalized ⊕-cofinitely supplemented module. insert ignore into journalissuearticles values(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