对偶τ-Rickart模  

Dualτ-Rickart modules

作　　者：李煜彦[1] 何东林[1] LI Yu-yan;HE Dong-lin(College 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：《兰州理工大学学报》2022年第3期169-172,共4页Journal of Lanzhou University of Technology

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(2020A-277,2021B-364)。

摘　　要：设τ=(T,F)表示遗传挠理论,引入了对偶τ-Rickart模的概念.称M是对偶τ-Rickart模,如果对任意ψ∈End(M),π^(-1)_(τ)(Im^(-)ψ)=Imψ+τ(M)是M的直和因子.研究了对偶τ-Rickart模的性质,给出了对偶τ-Rickart模的等价刻画.进而,证明了M是τ-Rickart模并且M/τ(M)具有C_(2)条件当且仅当M是对偶τ-Rickart模并且M/τ(M)具有D_(2)条件.Letτ=(T,F)be a hereditary torsion theory,the concept of dualτ-Rickart module is introduced.A module M is called dualτ-Rickart if π^(-1)τ(Im^(-)ψ)=Imψ+τ(M)is a direct summand of M for everyψ∈End(M).Properties of dualτ-Rickart module are studied,some equivalent characterizations to be dualτ-Rickart are given.Moreover,it is proved that M is τ-Rickart and M/(τ(M))has C_(2) condition if and only if M is dualτ-Rickart and M/(τ(M))has D_(2) condition.

关 键 词：对偶τ-Rickart模 τ-Rickart模 直和因子 

分 类 号：O153.3[理学—数学]