交换环上的w^(*)-模  

w^(*)-modules over commutative rings

作　　者：陶蕴芝 王芳贵 李建鸿 TAO Yunzhi;WANG Fanggui;LI Jianhong(School of Mathematical Science,Sichuan Normal University,Chengdu 610066,China)

机构地区：[1]四川师范大学数学科学学院,四川成都610066

出　　处：《南昌大学学报（理科版）》2022年第5期500-511,517,共13页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(11671283)。

摘　　要：设R是交换环,M是R-模,J是R的有限生成正则理想,若自然同态φ:R→J^(*)=Hom_(R)(J,R)是同构,则J称为R的GV^(*)-理想。用GV^(*)-理想定义了GV^(*)-无挠模,证明了无挠模是GV^(*)-无挠模。接着引入了w^(*)-模,模的w^(*)-包络,得到了正则w^(*)-理想与正则w-理想的等价性。作为应用,对w-Noether环和SM环进行了新的刻画,并证明了相应的w^(*)-版本的Cartan-Eilenberg-Bass定理。Let R be a commutative ring,M be a R-module and J be a finitely generated regular ideal of R.J is called a GV^(*)-ideal if the natural homomorphismφ:R→J^(*)=Hom_(R)(J,R)is an isomorphism.In this paper,we use GV^(*)-ideals to define GV^(*)-torsion-free modules,and prove that the torsion-free modules are GV^(*)-torsion-free modules.Then we introduce w^(*)-modules,w^(*)-closure of modules,and get the equivalence of regular w^(*)-ideals and regular w-ideals.As applications,we give some new characterizations of w-Noether rings and SM rings,and prove corresponding w^(*)-theoretic analogue of the Cartan-Eilenberg-Bass theorem.

关 键 词：GV^(*)-理想 GV^(*)-无挠模 w^(*)-模 w^(*)-包络 w-Noether环 SM环 

分 类 号：O153.3[理学—数学]