GENERALIZED PROJECTIVITY OF QUASI-DISCRETE MODULES

Year 2008, Volume: 3 Issue: 3, 125 - 134, 01.06.2008

Yosuke Kuratomi

Abstract

In 2004, S.H.Mohamed and B.J.Müller defined generalized projectivity (dual ojectivity) as follows: given modules A and B, A is generalized B-projective (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 (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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