环与剩余类环的同调维数

On Homological Dimensions of Rings and Residue Rings

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摘要ＳａｎｄｏｍｉｅｒｓｋｉＦ．Ｌ，ＳｍａｌｌＬ．Ｗ，和ＦｉｅｌｄｓＫ．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ＶｏｎＮｅｕｍａｎｎ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． 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.

作者朱晓胜杨静化

机构地区河海大学数理系中国药科大学数学教研室

出处《数学学报（中文版）》 SCIE CSCD 北大核心 2001年第5期777-784,共8页 Acta Mathematica Sinica：Chinese Series

基金国家自然科学基金资助项目(19771046)

关键词同调维数投射平坦约化环环剩余类环幂零 Homological dimension Projective Flat Residue ring

分类号 D153.3 [政治法律—国际共产主义运动]

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2[2]Small L. W., A Change of Rings Theorem [J], Proc. Amer. Math. Soc., 1968, 19: 662-666.
3[3]Fields K. L., On the Global Dimension of Residue Rings [J], J. Math., 1970, 32(2): 345-349.
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环与剩余类环的同调维数

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