广义τ-奇异模和τ-非奇异模  

Generalizedτ-singular andτ-nonsingular modules

作　　者：李煜彦[1] LI Yuyan(Department of Mathematics,Longnan Teachers College,Longnan Gansu 742500)

机构地区：[1]陇南师范高等专科学校数学系,甘肃陇南742500

出　　处：《首都师范大学学报（自然科学版）》2021年第2期7-9,共3页Journal of Capital Normal University：Natural Science Edition

基　　金：甘肃省高等学校创新能力提升项目(2019B-224);甘肃省高等学校科研项目(2018A-269)。

摘　　要：设τ是遗传挠理论,提出了广义τ-奇异和τ-非奇异的概念.称模M中的元素m是广义τ-奇异的,如果其右零化子annr(m)是环R的广义τ-本质右理想.称模M是广义τ-奇异(或广义τ-非奇异)的,如果其所有元素都是广义τ-奇异的(或唯一的广义τ-奇异元是0).讨论了模M的广义τ-奇异子模Zτ(M)的若干性质,给出了N■τM与M/N是广义τ-奇异的等价条件,证明了模M是广义τ-非奇异的,当且仅当对任意广义τ-奇异模N,Hom(N,M)=0.In this paper,the concept of generalizedτ-(non)singularity is introduced.An element m in a module M is called generalizedτ-singular if its right annihilator is a generalizedτ-essential right ideal in R.The module M is generalizedτ-singular(resp.generalizedτ-nonsingular)if all its elemenets are generalizedτ-singular(resp.if the only generalizedτ-singular element is 0).Some properties of Zτ(M)which is a generalizedτ-singular submudules of M are discussed,the equivalent condition of N■τM and M/N being generalizedτ-singular is given,it is proved that a module M is generalizedτ-nonsingular if and only if Hom(N,M)=0 for all generalizedτ-singular modules N.

关 键 词：广义τ-奇异 广义τ-非奇异 广义τ-本质子模 

分 类 号：O153[理学—数学]