|
- 2015
多项式环的表现维数
|
Abstract:
摘要: 设R为有单位元的环,M为右R-模,通过研究多项式环上的表现维数,得到了当R,R[x]为凝聚环时,MR与MR[x]的表现维数之间的关系以及R与R[x]的表现维数之间的关系等结论.
Abstract: Let R be a ring with a unit element, and M be a right R-Module. The relationship between FPd(MR) and FPd(MR[x]) as well as between FPD(R) and FPD(R[x]) are obtained by using the presented dimensions of polynomial rings, when R and R[x] are coherent rings
[1] | ZHOU Dexu, GONG Zhiwei. On presented dimensions of modules and rings[J]. International Journal of Mathematics and Mathematical Sciences, 2010:1-13. doi: 10.1155/2010/256267. |
[2] | COSTA D L. Parameterizing families of non-noetherian rings[J]. Communications in Algebra, 1994, 22(10):3997-4011. |
[3] | XUE Weimin. On n-presented modules and almost excellent extensions[J]. Communications in Algebra, 1999, 27(3):1091-1102. |
[4] | 李元林. 有限表现维数的换环定理[J]. 南京大学学报: 数学半年刊, 1990, 7(1):75-84. LI Yuanlin. Some theorems on chane of rings of the finitely presented dimension[J]. Journal of Nanjing University Mathematical Biquarterly, 1990, 7(1):75-84. |
[5] | 周伯壎. 同调代数[M]. 北京: 科学出版社, 1988. ZHOU Boxun. Homological algebra[M]. Beijing: Science Press, 1988. |
[6] | 程福长, 易忠. 环的同调维数[M]. 桂林: 广西师范大学出版社, 2000. CHENG Fuchang, YI Zhong. Homological dimension of rings[M]. Guilin: Guangxi Normal University Press, 2000. |
[7] | 李元林. F.P.-维数的合冲定理[J]. 数学研究与评论, 1993, 13(2): 283-288. LI Yuanlin. Syzygy theory of F.P.-dimension[J]. Journal of Mathematical Research and Exposition, 1993, 13(2):283-288. |