凝聚多项式扩张的Whitehead群(英文)  

The Whitehead Groupof a Coherent Polynomial Extension

作　　者：赵伟[1] 

机构地区：[1]阿坝师范高等专科学校数学研究所//数学与财经系,汶川四川623002

出　　处：《内江师范学院学报》2014年第6期1-6,共6页Journal of Neijiang Normal University

基　　金：国家自然科学基金(11171240,11161006);四川省教育厅项目(14ZB0335);四川高校科研创新团队支持计划(14TD0040);阿坝师专专项课题(ASB13-18)

摘　　要：应用K1群的转化定理可以证明有限表现模范畴与有限生成投射模范畴的Whitehead群同构.从而可以证明一个正则稳定凝聚环与其上的多项式环的Whitehead群同构.作为推论,此结果对于广义伞环成立.The resolution theorem for K1 implies that the whitehead groups of the categories of finitely presented modules and the categories of finitely generated projective modules over a coherent ring are isomorphic. From this it is obtained that the whitehead groups of a regular stably coherent ring R and the polynomial ring over R are isomorphic. As corollary, this result also holds for true any generalized umbrella ring R.

关 键 词：Whitehead群 凝聚环 正则环 

分 类 号：O153.3[理学—数学]