Frobenius扩张下的G_(C)-平坦性  

G_(C)-Flatness under Frobenius Extensions

作　　者：周绪杰 赵志兵[1] ZHOU Xujie;ZHAO Zhibing(School of Mathematical Sciences,Anhui University,Hefei 230601,China)

机构地区：[1]安徽大学数学科学学院,合肥230601

出　　处：《吉林大学学报（理学版）》2022年第4期800-804,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11871071);安徽省高校自然科学研究重点项目(批准号:KJ2019A0007).

摘　　要：设A/S是一个环的Frobenius扩张,且S是凝聚环,C是半对偶S-模.首先,利用构造法证明相对于半对偶模的G_(C)-平坦性在环的Frobenius扩张下是保持的,即对于A-模M,M_(A)是G_(C■_(S)A)-平坦模当且仅当M_(S)是G_(C)-平坦的;其次,证明相对于半对偶模的G_(C)-平坦维数在环的Frobenius扩张下是不变的.Let A/S be a Frobenius extension of rings with S coherent and C a semidualizing S-module.Firstly,we prove that G_(C)-flatness with respect to a semidualizing module is invariant under Frobenius extensions by using the construction method,that is,for an A-module M,M_(A) is G_(C■_(S)A)-flat module if and only if M_(S) is G_(C)-flat.Secondly,we prove that G_(C)-flat dimension with respect to a semidualizing module is preserved under Frobenius extensions.

关 键 词：半对偶模 G_(C)-平坦模 G_(C)-平坦维数 Frobenius扩张 

分 类 号：O154.2[理学—数学]