Noether环上的幂稳定自由模

数学物理学报 ›› 2008, Vol. 28 ›› Issue (6): 1227-1231.

Noether环上的幂稳定自由模

陈焕艮|张卫

(湖南师范大学数学系长沙 410081)

收稿日期:2006-09-15 修回日期:2007-06-11 出版日期:2008-12-25 发布日期:2008-12-25
通讯作者: 陈焕艮
基金资助:
湖南省自然科学基金(08JJ3006)资助

Power Stably Free Modules over Noetherian Rings

Chen Huanyin|Zhang Wei

(Department of Mathematics, Hunan Normal University, Changsha 410006)

Received:2006-09-15 Revised:2007-06-11 Online:2008-12-25 Published:2008-12-25
Contact: Chen Huanyin

摘要/Abstract

摘要：

设I是Noether环R的投射理想, I^m=Iⁿ, m≠n. 该文证明, 有限生成投射右R - 模幂稳定自由当且仅当(1) 存在环S使得I^|m-n|( S ( R且有限生成投射S - 模是幂稳定自由; (2) 有限生成投射右R/I^|m-n|- 模幂稳定自由.

关键词: Noether 环, 幂稳定自由, K₀-群

Abstract:

Let I be a projective ideal of a noetherian ring R and I^m=Iⁿ for some m≠n. We prove that every finitely generated projective right R-module is power stably free if and only if (1) there exists a ring S such that I^|m-n|( S ( R and every finitely generated projective right S-module is power stably free, and (2)every finitely generated projective right R/I^|m-n|-module is power stably free.

Key words: Noetherian ring, Power stably free, K₀-group

中图分类号:

16D40

陈焕艮|张卫. Noether环上的幂稳定自由模[J]. 数学物理学报, 2008, 28(6): 1227-1231.

Chen Huanyin|Zhang Wei. Power Stably Free Modules over Noetherian Rings[J]. Acta mathematica scientia,Series A, 2008, 28(6): 1227-1231.