摘要
As we all know, the properties of ring are determined by its right unital modules category. Sometimes we only want to know the properties of a certain module. So one may very naturally ask whether the properties of arbitrary right unital module M_R can be determined by the properties of its Fuller category σ[M_R], where σ[M_R] is a minimal full subcategory of Mod-R which contains M_R and is closed under submodules, homomorphic images and direct sums. This work was begun by Fuller and was continued by many famous mathematicians. Now, we introduce a character of σ[M_R] which ensures that M_R has finite length and σ[M_R] is equivalent to a right module category of some right Artinian rings and also give an application of this results.
