FI-扩张环和模的推广  

Generalization of FI-extending Rings and Modules

作　　者：李煜彦[1] 王奇临 LI Yuyan;WANG Qilin(School of Mathematics and Information Sciences,Longnan Teachers College,Longnan 742500,China)

机构地区：[1]陇南师范高等专科学校数信学院,甘肃陇南742500

出　　处：《湖北民族大学学报（自然科学版）》2021年第2期218-222,共5页Journal of Hubei Minzu University:Natural Science Edition

基　　金：甘肃省高等学校创新能力提升项目(2019B-224);甘肃省高等学校创新基金项目(2020A-277).

摘　　要：设τ是遗传挠理论.提出了τ-FI-扩张环和模的概念,它是FI-扩张环和模的推广.称M是τ-FI-扩张模,如果对M的任意全不变τ-稠密子模N,存在M的直和因子K,使得N是K的τ-本质子模.研究了τ-FI-扩张环和模的性质,给出了τ-FI-扩张模关于直和因子封闭的局部条件,证明了右τ-FI-扩张环上的某些循环模仍是τ-FI-扩张模.进而,讨论了τ-FI-扩张模以及右τ-FI-扩张环关于本质扩张的遗传性质.Letτbe a hereditary torsion theory.The concepts ofτ-FI-extending ring and module are introduced,which are generalization of FI-extending ring and module.A module M is called aτ-FI-extending module if for every fully invariantτ-dense submodule N of M,there exists a direct summand K of M,such that N isτ-essential in K.Some properties ofτ-FI-extending ring and module are studied,and several local conditions are given to show thatτ-FI-extending module is closed under the direct summand,it is proved that certain cyclic modules of a rightτ-FI-extending ring also haveτ-FI-extending.Moreover,the hereditary properties of essential extension ofτ-FI-extending modules and rightτ-FI-extending rings are discussed.

关 键 词：遗传挠理论 τ-FI-扩张模 τ-补 τ-全不变子模 

分 类 号：O153[理学—数学]