τ-Rickart模  

τ-Rickart Modules

作　　者：李煜彦[1] LI Yu-yan(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：《西北民族大学学报（自然科学版）》2021年第2期1-3,50,共4页Journal of Northwest Minzu University(Natural Science)

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：文章研究τ-Rickart模的性质,讨论τ-Rickart模关于子模的封闭性,并举例说明τ-Rickart模的直和未必是τ-Rickart模,给出了τ-Rickart模的直和仍是τ-Rickart模的条件.进而,证明若M是τ-Rickart模且是投射(或内射)模,则对M的任意直和因子K,τ(M)+K是投射(或内射)模.Properties ofτ-Rickart module are studied,the closure ofτ-Rickart modules with respect to submodules is also discussed,an example is given to show that the direct sum ofτ-Rickart modules may not beτ-Rickart module,and the conditions that direct sum ofτ-Rickart modules is alsoτ-Rickart are given.Moreover,it is proved that if M be aτ-Rickart and projective(injective)module,then for every direct summand K of M,τ(M)+K is also a projective(injective)module.

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]