Application Of Contravariantly Finite Subcategory Closed Under Predecessors

Let A be an Artin algebra and mod A be the category of all finitely gen-erated right A-modules.This paper mainly discuss the contravariantly finite subcategory,closed under predecessor.As a main result,let H,B be path algebra and tilted algebra over an algebra closed field,respectively.we discuss the rela-tion of both of the connected subcategories in the preinjective partition.This paper is composed of four chapters:In the first chapter, we introduce the relevant background and give our main result;In the second chapter,we list a number of related concepts,propositions and theorems;In the third chapter,we prove our main theorem;In the forth chapter,we illustrate its application with some examples.