模子范畴间的对偶

Duality between Subcategories of Modules

针对模论中两类重要的模子范畴:投射模范畴与内射模范畴,以及模论中两个重要的概念:sm all模和self-sm all模,对偶地引入了co-sm all模和co-self-sm all模的概念,给出了这两类范畴间对偶的等价刻画,特别地,给出了在Noether情形下余-*-模的刻画.

Categories of projective modules and categories of injective modules are two important class in the theory of modules. Small module and self-small module are two important concepts in the theory of modules. The concepts of co-small module and co-self- small module are introduced in this paper. Duality between the categories of projective modules and the categories of injective modules is given. In particular,in the ease of Noether, some characterizations on co- ＊ -module are presented.