正则Noether环  

Large Regular Noetherian Rings

作　　者：齐薇 张晓磊 QI Wei;ZHANG Xiaolei(School of Mathematics and Statistics,Shandong University of Technology,Zibo Shandong 255000,China)

机构地区：[1]山东理工大学数学与统计学院,山东淄博255000

出　　处：《重庆师范大学学报（自然科学版）》2023年第5期113-117,共5页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金青年科学基金项目(No.12201361);国家自然科学基金地区科学基金项目(No.12061001)。

摘　　要：设R是交换环,若R的任意正则理想都是有限生成的,则称R是正则Noether环。首先研究了多项式环的正则Noether性质。特别地,举例说明R是正则Noether环,R[x]不一定是正则Noether环。其次,研究了合并代数的正则Noether性质。最后,通过正则内射模和正则余平坦模刻画了正则Noether环。Let R be a commutative ring.Then R is said to be a regular Noetherian ring provided that any regular ideal is finitely generated.The regular Noetherian properties of polynomial rings are obtained.In particular,an example of a regular Noetherian ring R is given to show that RαJ need not be regular Noetherian.Then the regular Noetherian properties of amalgamation algebras is studied.Finally,regular Noetherian rings are characterized in terms of regular injective modules and regular coflat modules.

关 键 词：正则Noether环 Hilbert基定理 合并代数 正则内射模 正则余平坦模 

分 类 号：O154.2[理学—数学]