Properties Of Injective Objects In The Category Of Riesz Spaces On Left R-modules

In the 1920 s and 1930 s,F.Riesz introduced lattice structure into vector space,which marked the beginning of Riesz space research.Based on the study that on some Properties of Riesz Spaces on Left R-modules,we gave the concept of injective objects in the Category of Riesz Spaces on Left R-modules,and studied the separability of injective objects in the category of Riesz spaces on left R-modules,a product of a bunch of Riesz Spaces on Left R-modules is an injective object if and only if every one is an injective object is proved.The main contents of this paper are as follows:In Chapter 1,we introduce the background and basic definition of the research on the properties of Riesz Spaces on Left R-modules.In Chapter 2,the basic and special properties of Riesz Spaces on Left R-modules are studied under the background of related properties of Riesz Spaces on Left R-modules.In Chapter 3,by studying the properties of Riesz Spaces on Left R-modules,the concept of the Category of Riesz Spaces on Left R-modules is introduced.By using the language of category,the representation of monk morphism and epimorphism of the Category of Riesz Spaces on Left R-modules and their exact sequence,the basic lemma of the Category of Riesz Spaces on Left R-modules is proved.In Chapter 4,Based on the Study that on some Properties of Riesz Spaces on Left R-modules,we gave the concept of injective objects in the Category of Riesz Spaces on Left R-modules,a product of a bunch of Riesz Spaces on Left R-modules is an injective object if and only if every one is an injective object is proved.