环与剩余类环的同调维数

朱晓胜;杨静化

数学学报 ›› 2001, Vol. 44 ›› Issue (5) : 777-784.

PDF(348 KB)
PDF(348 KB)
数学学报 ›› 2001, Vol. 44 ›› Issue (5) : 777-784. DOI: 10.12386/A2001sxxb0100
论文

环与剩余类环的同调维数

    朱晓胜;杨静化
作者信息 +

On Homological Dimensions of Rings and Residue Rings

    Xiao Sheng ZHU(1),Jing Hua YAN
Author information +
文章历史 +

摘要

Sandomierski F.L,Small L.W,和 Fields K.L.[1-2]在“幂零”条件下研究了环与约化环的同调维数.然而对一些环(如交换 Von Neumann正则环),“幂零’的条件是不成立的.因此,在本文中我们考虑非“幂零”条件下(如R(R/I)((R/I)R)是R-投身的或R(R/I)R是R-平坦的),环与约化环的同调维数.

Abstract

The authors of Sandomierski F. L., Small L. W., Fields K. L.[1-3] studied homological dimensions of rings and residuce rings under "nilpotent" conditions. But, for some rings (for example, R is a commutative Von Neuman regular ring) the "nilpo- tent" conditions don't hold. Hence, in this paper, we consider homological dimensions of rings and residuce rings under "no-nilpotent" conditions such as R(R/t)((R/I)R) is R-projective of R(R/I)R is R-flat.

关键词

同调维数 / 平坦 / 约化环 / 投射

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朱晓胜;杨静化. 环与剩余类环的同调维数. 数学学报, 2001, 44(5): 777-784 https://doi.org/10.12386/A2001sxxb0100
Xiao Sheng ZHU(1),Jing Hua YAN. On Homological Dimensions of Rings and Residue Rings. Acta Mathematica Sinica, Chinese Series, 2001, 44(5): 777-784 https://doi.org/10.12386/A2001sxxb0100
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