关于强可分扩张的注记（英文）  

NOTES ON STRONGLY SEPARABLE EXTENSIONS

作　　者：徐爱民[1] XU Aimin(School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China)

机构地区：[1]曲阜师范大学数学科学学院,山东曲阜273165

出　　处：《数学杂志》2018年第1期25-33,共9页Journal of Mathematics

基　　金：Supported by Supported by National Natural Science Foundation of China(11401339);NSF of Shandong Province of China(ZR2014AQ024);Youth Foundation and Doctor’s Initial Foundation of Qufu Normal University(Xkj201401;BSQD2012042)

摘　　要：设R和S是环,?:R→S是强可分扩张.本文研究了(Gorenstein)整体维数和表示型在R与S之间的关系.利用同调方法,证明了(1)R与S有相同的左整体维数,左弱整体维数,左Gorenstein整体维数;(2)若R和S是阿丁代数,则R是CM-有限的(CM-自由的,有限表示型)当且仅当S是CM-有限的(CM-自由的,有限表示型),推广了已知的结果.Let R and S be rings and':R!S a strongly separable extension.In this paper,we study the relationship of(Gorenstein)global dimensions and representation type between R and S.By using the homological methods,we proved that(1)R and S have the same left global dimension,left weak global dimension,left Gorenstein global dimension;(2)Assume that R and S are Artin algebras,then R is CM-ˉnite(resp.,CM-free,ofˉnite representation type)if and only if so is S,which generalize some known results.

关 键 词：强可分扩张 左Gorenstein整体维数 CM-有限的 

分 类 号：O154.2[理学—数学]