相关于挠理论的(拟)连续模  

(Quasi-)Continuous Modules Relative to the Torsion Theory

作　　者：李煜彦[1] 何东林[1] LI Yu-yan;HE Dong-lin(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：《五邑大学学报（自然科学版）》2020年第3期12-15,21,共5页Journal of Wuyi 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M,N是R-Mod,τ=(T,F)是遗传挠理论,提出了模M是τ-N-(拟)连续模的概念,它是(拟)连续模的推广.给出了模M是τ-N-extending模的等价刻画,并对短正合序列0→N1→N→N2→0,证明了M是τ-N-(拟)连续模当且仅当M是τ-N1和τ-N2-(拟)连续模.Let M,N be R-Mod,andτ=(T,F)be a hereditary torsion theory.In this paper,the concept that M as aτ-N-(quasi-)continuous module is introduced,which is a generalization of the(quasi-)continuous module,and some equivalent characterizations ofτ-N-extending module are given.Moreover,let 0→N1→N→N2→0 be an exact sequence,the paper proves that M is aτ-N-(quasi-)continuous module if and only if it is bothτ-N1-(quasi-)continuous andτ-N2-(quasi-)continuous.

关 键 词：遗传挠理论 (拟)连续模 直和因子 τ-补 

分 类 号：O153.3[理学—数学]