The FP-Projective Modules and FP-Injective Modules Under Ring Transformation

The extension of rings and modules is one of the basic problems in the research of rings and categories of modules.Some ring transformations induced by ring homomorphisms can make a module over one ring inherit a module structure over another.The projectivity and injectivity are kept under many extensions of rings,and they can also be passed though ring transformations.As generalizations of them,the author mainly discusses the properties of FP-projective modules and FP-injective modules under ring transformation in this paper.