The Auslander Formula Over Coherent Rings

It is well known that a lot of results about finitely generated modules over Noethe-rian rings can be extended to finitely presented modules over coherent rings. In this thesis, the main aim is to study the Auslander formula on finitely presented modules over coherent rings and make its generalization on this basis.In Chapter 1, we give some notions and notations which will appear in the following chapters.In Chapter 2, we give some equivalent characterizations of the Auslander condition over coherent rings. A generalization of the Auslander formula is the important point of this chapter, which is under the condition:ExtΛopt(ExtΛκ(M,Λ),Λ)=0, whereκ≥1,t≥0 and M∈modΛ.In Chapter 3, we study some special cases of the generalization of Auslander formula, and obtain some equivalent characterizations of the Auslander-type condition.