Cotorsion Pair Extensions  

作　　者：De Xu ZHOU 

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

出　　处：《Acta Mathematica Sinica,English Series》2009年第9期1567-1582,共16页数学学报（英文版）

基　　金：Supported by Natural Science Foundation of China (Grant No. A0324656);Natural Science Foundation of Fujian Province (Grant No. 2009J01003);Scientific Research Foundation of Fujian Provincial Department of Science and Technology (Grant No. 2007F5038);Foundation of Fujian Normal University (Grant Nos. 2008100209, 09A004)

摘　　要：Assume that S is an almost excellent extension of R. Using functors HomR（S,-） and -×R S, we establish some connections between classes of modules lR and lS, cotorsion pairs （AR, BR） and （AS, BS）. If lS is a T-extension or （and） H-extension of lR, we show that lS is a （resp., monomorphic, epimorphic, special） preenveloping class if and only if so is lR. If （AS, BS） is a TH- extension of （AR, BR）, we obtain that （AS, BS） is complete （resp., of finite type, of cofinite type, hereditary, perfect, n-tilting） if and only if so is （AR, BR）.Assume that S is an almost excellent extension of R. Using functors HomR（S,-） and -×R S, we establish some connections between classes of modules lR and lS, cotorsion pairs （AR, BR） and （AS, BS）. If lS is a T-extension or （and） H-extension of lR, we show that lS is a （resp., monomorphic, epimorphic, special） preenveloping class if and only if so is lR. If （AS, BS） is a TH- extension of （AR, BR）, we obtain that （AS, BS） is complete （resp., of finite type, of cofinite type, hereditary, perfect, n-tilting） if and only if so is （AR, BR）.

关 键 词：cotorsion pair ring extension preenveloping class 

分 类 号：O153.3[理学—数学] S663.1[理学—基础数学]