Covering Morphisms in a Pushout-Pullback Diagram  

作　　者：De Xu ZHOU 

机构地区：[1]Department of Mathematics, Fujian Normal University, Fujian 350007, P. R. China

出　　处：《Journal of Mathematical Research and Exposition》2010年第3期536-542,共7页数学研究与评论（英文版）

基　　金：Supported by the Natural Science Foundation of Fujian Province (Grant No. 2009J01003);the Foundation of Fujian Normal University (Grant No. 2008100209);partially by the Open Funds of Key Lab of Fujian Province University Network Security and Cryptology (Grant No. 09A004)

摘　　要：In a pushout-pullback diagram, which consists of four morphisms f ： A → B, g ： A → C, α ： C → D and β ： B → D, we give some relations among the covers of these four modules. If ker f∈I（ ）, then g ： A → C is -covering if and only if ： B → D is -covering. If every module has an -precover and kerf E I（ ）, then A and C have isomorphic -precovers if and only if B and D have isomorphic -precovers.In a pushout-pullback diagram, which consists of four morphisms f ： A → B, g ： A → C, α ： C → D and β ： B → D, we give some relations among the covers of these four modules. If ker f∈I（ ）, then g ： A → C is -covering if and only if ： B → D is -covering. If every module has an -precover and kerf E I（ ）, then A and C have isomorphic -precovers if and only if B and D have isomorphic -precovers.

关 键 词：COVER covering morphism pushout-pullback diagram. 

分 类 号：O153.3[理学—数学]