GENERALIZED PROJECTIVITY OF QUASI-DISCRETE MODULES

Authors : Yosuke KURATOMİ

Pages : 125-134

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Publication Date : 2008-06-01

Article Type : Research Paper

Abstract :In 2004, S.H.Mohamed and B.J.Müller defined generalized projectivity insert ignore into journalissuearticles values(dual ojectivity); as follows: given modules A and B, A is generalized B-projective insert ignore into journalissuearticles values(B-dual ojective); if, for any homomorphism f : A → X and any epimorphism g : B → X, there exist decompositions A = A0 ⊕ A00, B = B0⊕B00, a homomorphism ϕ : A0 → B0 and an epimorphism ψ : B00 → A00 such that g ◦ ϕ = f|A0 and f ◦ ψ = g|B0 . Generalized projectivity plays an important role in the study of direct sums of lifting modules. Since the structure of generalized projectivity is complicated, it is difficult to determine whether generalized projectivity is inherited by insert ignore into journalissuearticles values(finite); direct sums. This problem is not easy even in the case that each module is quasi-discrete. In this paper we consider this problem.
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