Gorenstein投射子范畴上的AR-问题

本项目主要是拟利用Auslander-Reiten理论中的Irreducible morphism理论、相对同调函子理论和有限维代数上的导出范畴理论来系统地研究Goresntein投射子范畴上的 Auslander-Reiten问题，即：在Artinian代数上，一个有限生成Gorenstein投射模是投射的当且仅当它是自正交模;在交换Noetheian环上，一个有限生成的Goresntein投射模时投射的当且仅当它是自正交模。这些研究将为解决Auslander-Reiten问题提供新的研究角度和方法。

In this project, we shall use the theories of Irreducible morphisms of Auslander-Reiten theory, the relative homological functors and the derived category on finite dimension algebras invented as tools to study systematically the Auslander-Reiten Question on the Gorenstein projective subcategory. That is, for Artinian algebras, a finitely generated Gorenstein projective module is projective if and only if it is selforthogonal;for commutative Noetherian rings, a finitely generated Gorenstein projective module is projective if and only if it is selforthogonal. We wish to give new ideas in Auslander-Reiten Question.