Some Special Modules Under Faithfully Flat Ring Extensions

In this paper,some special modules under faithfully flat ring extensions are main?ly investigated.The first chapter is the introduction and preparatory knowledge.In the second chapter,strongly cotorsion modules under faithfully flat ring extensions are inves-tigated.Let R be a commutative noetherian ring and S be a faithfully flat R-algebra.It is proved that,under some extra assumptions,an R-module G is strongly cotorsion if and only if HomR(S,G)is a strongly cotorsion R-module and ExtR>0(S,G)= 0 if and only if HomR(S,G)is a strongly cotorsion S-module and ExtR>0(S,G)= 0.In the third chap-ter,cotorsion modules under faithfully flat ring extensions are investigated.In the fourth chapter,Gorenstein cotorsion modules under faithfully flat ring extensions are investigat-ed.In the fifth chapter,Some results about cotorsion modules and Gorenstein cotorsion modules are supplemented.