对偶扩张代数的分裂挠理论与Generic模  

SPLITTING TORSION THEORIES AND Generic MODULES OVER DUALEXT ENSION ALGEBRAS

作　　者：杜先能[1] 

机构地区：[1]安徽大学数学系,合肥230039

出　　处：《数学年刊（A辑）》2002年第5期547-554,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10071062);安徽省自然科学基金资助的项目.

摘　　要：设A是一个有限维代数,R是A的对偶扩张代数.MA是一个A-模.给定一个倾斜R-模M（?）AR,我们知道MA一定是一个倾斜A-模 设（TM（?）AR,FM（?）AR）与（TM,FM）是分别由M（?）AR和MR导出的挠理论.本文讨论挠理论的分裂性以及GenericA-模与GenericR-模之间的关系.Let A be a finite-dimensional algebra, R the dual extension of A and MA an A-module. Given a tilting R-module M (?)A R, it is known that M must be a tilting A-module. Let (TM(?)AR,FM(?)AR) and (TM,FM) be the torsion theories induced by M (?)A R and MR respectively. In the present paper, the author investigates the splitness of the torsion theory, and the relationship between Generic A-module and Generic R-module.

关 键 词：对偶扩张 分裂挠理论 Generic模 

分 类 号：O153.3[理学—数学]