Gorenstein N Flat Modules Over Formal Triangular Matrix Rings

Let n be a nonnegative integer and(?)a formal triangular matrix ring.Based on many previous work of predecessors,in this thesis,we investigate n-absolltely pure T-modules,n-flat T-modules and n-cotorsion T-modules.Fur-thermore,we investigate Gorenstein n-flat T-modules.This paper consists of five chapters.In chapter 1,we introduce the background and the main results of the thesis,and give some basic definitions and facts needed in the later chapters.In chapter 2,by means of the conclusions of projective modules and finitely presented modules over formal triangular matrix rings,we investigate n-absolutely pure modules over formal triangular matrix rings.In particular,under some mild conditions,we prove that L=(L1,L2)is a n-absolutely pure right T-module,then L1 is a n-absolutely pure right A-module and L2 is n-absodutely pure right B-module.In chapter 3,by means of the conclusions of projective modules and finitely presented modules over formal triangular matrix rings,we investigate n-flat modules over formal triangular matrix rings.In particular,under some mild conditions,we prove that(?)is a n-flat left T-module,then M1 is a n-flat left A-module and M2 is n-flat left B-module.In chapter 4,by means of the conclusions of n-flat modules over formal triangu-lar matrix rings,we investigate n-cotorsion modules over formal triangular matrix rings.In particular,under some mild conditions,we prove that(?)is a n-cotorsion left T-module,then N1 is a n-cotorsion left A-module and N2 is n-cotorsion left B-module.In chapter 5,by means of the conclusions of n-absolutecy pure modules and n-flat modules over formal triangular matrix rings,we investigate Gorenstein n-flat modules over formal triangular matrix rings.In particular,under some mild conditions,we prove that M=(?)is a Gorenstein n-flat left T-module,then M1 is a Gorenstein n-flat left A-module.