Homological Properties Of Several Type Of Modules Over Formal Triangular Matrix Rings

Projective modules and injective modules play important roles in homological algebras and module theory.Recently,generalized projective modules and generalized injective modules were widely investigated by many authors.In addition,formal triangular matrix rings as a natural generalization of rings are important,they are used to construct the counter examples,This makes the theory of rings and modules more abundant and concrete.This dissertation is inspired by combination of these knowledge.This paper mainly studies homological properties of several types of modules over formal triangular matrix rings.Firstly,by means of the conclusion of projective modules and injective modules over formal triangular matrix rings of order 2,the characterization of n-Gorenstein projective modules over formal triangular matrix rings of order 2 is investigated.Secondly,by means of the characterization of duality pairs over formal triangular matrix rings of order 2,the characterization of duality pairs over formal triangular matrix rings of order 3 is researched.Finally,by means of the characterization of FP-injective modules over formal triangular matrix rings of order 2,the FP-injective modules over formal triangular matrix rings of order 3 are described.