Gorenstein内射Phantom态射

Gorenstein Injective Phantom Morphism

本文引入了Gorenstein内射Phantom态射和高维Gorenstein内射Phantom态射的概念,研究了Gorenstein内射Phantom态射的性质:在H(R)中,Gorenstein内射Phantom态射的类关于直积和ME-扩张封闭.证明了:R-模态射φ:XX′是高维Gorenstein内射Phantom态射当且仅当在态射范畴中存在φ的Gorenstein内射分解,使得它的n次余合冲是Gorenstein内射Phantom态射.

In this thesis,the concepts of Gorenstein injective Phantom morphism and higher Gorenstein injective Phantom morphism have been introduced,some properties of Gorenstein injective Phantom morphism been studied,and the class of Gorenstein injective Phantom morphisms been closed under direct product and ME-extensions in H(R).It is proved that a morphismφ:XX′of R-modules is higher Gorenstein injective Phantom morphism if and only if there is a Gorenstein injective resolution ofφin H(R)such that its n-th cosyzygy is a Gorenstein injective Phantom morphism.