相关于遗传挠理论的Rickart模  

Rickart Modules Relative to Hereditary Torsion Theory

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）》2020年第3期293-296,共4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=(T,F)表示遗传挠理论.受Ceken和Ebrahimi等人给出的τ-本质子模和t-Rickart模概念的启发,提出了τ-Rickart模的概念,它是t-Rickart模的推广.利用环模理论的方法,研究了τ-Rickart模的性质,讨论了τ-Rickart模与Rickart模之间的关系,给出了τ-Rickart模的等价刻画.进而,讨论了τ-Rickart模和τ-Baer模的等价条件.Letτ=(T,F)denote a hereditary torsion theory.Inspired by the concept ofτ-essential modules and t-Rickart modules given by Asgari and Ebrahimi et al,the concept ofτ-Rickart module is introduced,which is a generalization of t-Rickart module.Using methods of rings and modules theory,several properties ofτ-Rickart modules are studied,the relations betweenτ-Rickart module and Rickart Module are discussed,and some equivalent characterizations ofτ-Rickart modules are given.Moreover,The equivalent conditions ofτ-Rickart module andτ-Baer module are discussed.

关 键 词：t-Rickart模 τ-Rickart模 τ-Baer模 直和因子 

分 类 号：O153.3[理学—数学]