三角矩阵环上的absolutely clean模与GorensteinAC-平坦模  

Absolutely clean modules and Gorenstein AC flat modules over formal triangular matrix rings

作　　者：狄振兴 李晓曼 DI Zhen-xing;LI Xiao-man(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《山东大学学报（理学版）》2020年第12期81-88,96,共9页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11601433,11971388)。

摘　　要：设T=(A 0U B),其中A,B是环,U是左B右A双模。研究了absolutely clean T-模与Gorenstein AC-平坦T-模。在一定条件下,证明了L=(L1,L2)是absolutely clean右T-模,则L1是absolutely clean右A-模且L2是absolutely clean右B-模。作为这个结果的应用,在一定条件下,进一步证明了M=(M1M2)φM是Gorenstein AC-平坦左T-模当且仅当M1是Gorenstein AC-平坦左A-模,M2/ImφM是Gorenstein AC-平坦左B-模并且φM是单同态。Let T=(A 0U B)be a formal triangular matrix ring,where A and B are rings and U is a(B,A)-bimodule.In this article,we investigate absolutely clean T-modules and Gorenstein AC-flat T-modules.More specifically,under some mild conditions,we prove that L=(L1,L2)is absolutely clean right T-module then L1 is absolutely clean right A-module and L2 is absolutely clean right B-module.As an application of this result,under some conditions,we show that M=(M1M2)φM is Gorenstein AC flat left T-module if and only if M1 is a Gorenstein AC flat left A-module,M2/ImφM is a Gorenstein AC flat left B-module and the morphismφM is a monomorphism.

关 键 词：absolutely clean模 GORENSTEIN AC-平坦模 三角矩阵环 

分 类 号：O153.3[理学—数学]