[1]何 可,王芳贵*,沈 磊.TF-投射模与TF-投射维数[J].四川师范大学学报(自然科学版),2018,(04):456-462.[doi:10.3969/j.issn.1001-8395.2018.04.005]
 HE Ke,WANG Fanggui,SHEN Lei.TF- projective Modules and TF- projective Dimension[J].Journal of SichuanNormal University,2018,(04):456-462.[doi:10.3969/j.issn.1001-8395.2018.04.005]
点击复制

TF-投射模与TF-投射维数()
分享到:

《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2018年04期
页码:
456-462
栏目:
基础理论
出版日期:
2018-04-15

文章信息/Info

Title:
TF- projective Modules and TF- projective Dimension
文章编号:
1001-8395(2018)04-0456-07
作者:
何 可 王芳贵* 沈 磊
四川师范大学 数学与软件科学学院, 四川 成都 610066
Author(s):
HE Ke WANG Fanggui SHEN Lei
College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Sichuan
关键词:
无挠模 TF-投射模 TF-投射维数 余挠理论 余纯投射模 D-平坦模(强)P-凝聚环
Keywords:
torsionfree modules TF- projective modules TF- projective dimension cotorsion theory copure projective modules D projective dimension cotorsion theory copure projective modules lt moduels(strong)P-coherence ring
分类号:
O154
DOI:
10.3969/j.issn.1001-8395.2018.04.005
文献标志码:
A
摘要:
利用非交换环上的无挠模的概念,引入TF-投射模,也定义相应的同调维数.称左R-模M为TF-投射模,是指对任何无挠模T,都有Ext1R(M,T)=0.讨论TF-投射模与D-平坦模的关系,证明TF-投射整体维数为0的环都是QF环.最后,用TF-投射模维数刻画右强P-凝聚左Noether环.
Abstract:
In this article, we introduce the concept of TF-projective modules and TF-projective dimension of modules and rings in terms of the notation of torsionfree modules on non-commutative rings.That is, a right R- module is called TF-projective in case that Ext1R(M,N)=0 for any torsionfree module N.Some properties of TF-projective modules are given such as the ralation between TF-projective moduels and D-flat moduels.We also prove that rings of TF-projective dimension zero are QF rings.Some characterizations of left strong P-coherent and right Noether rings are given.

参考文献/References:

[1] 王芳贵.交换环与星型算子理论[M].北京:科学出版社,2006.
[2] GOODEARL K R.Ring Theory:Nonsingular Rings and Modules[M].New York:Marcel Dekker,1976.
[3] HATTORI A.A foundation of torsion theory for modules over general rings[J].Nagoya Math J,1960,17(17):147-158.
[4] STONE D R.Torsion-free and divisible modules over matrix rings[J].Pacific J Math,1970,35(1):235-253.
[5] BICAN L, EL BASHIR R, ENOCHS E E.All modules have flat covers[J].B London Math Soc,2001,33(4):385-390.
[6] GÖBEL R, TRLIFA J J.Approximations and Endomorphism Algebras of Modules[M].Berlin:Walter de Gruyter,2006.
[7] MAO L X, DING N Q.On divisible and torsionfree modules[J].Commun Algebra,2008,36(2):708-731.
[8] ROTMAN J J.An Introduction to Homological Algebra [M].New York:Academic Press,1979.
[9] ENOCHS E E, JENDA O M G.Relative Homological Algebra[M].Berlin:De Gruyter,2000.
[10] ANDERSON D D, FULLER K R.Rings and Categories of Modules[M].Berlin:Spring-Verlag,1974.
[11] FU X H, ZHU H Y, DING N Q.On copure projective modules and copure projective dimensions[J].Commun Algebra,2012,40(1):343-359.
[12] MAZUREK R, ZIEMBOWSKI M.On Bézout and distributive generalized power series rings[J].J Algebra,2006,306(2):397-411.
[13] ZHU H Y, DING N Q.Generalized morphic rings and their applications[J].Commun Algebra,2007,35(9):2820-2837.
[14] NICHOLSON W K, CAMPOS E S.Rings with the dual of the isomorphism theorem[J].J Algebra,2004,271(1):391-406.
[15] XU J Z.Flat Covers of Modules[M].Berlin:Springer-Verlag,1996.
[16] HU J S, DING N Q.Some results on torsionfree modules[J].J Algebra and Its Appl,2013,12(1):221-241.
[17] 陈建龙,张小向.凝聚环与FP-内射环[M].北京:科学出版社,2014.
[18] JENSEN C U, SIMSON D.Purity and generalized chain conditions[J].J Pure & Applied Algebra,1979,14(3):297-305.
[19] 施莉娜,王芳贵,熊涛.∞-余纯投射模[J].四川师范大学学报(自然科学版),2016,39(4):479-483.
[20] 熊涛,王芳贵,胡葵.余纯投射模与CPH环[J].四川师范大学学报(自然科学版),2013,36(2):198-201.
[21] 熊涛.余纯投射模与模的单平坦包[D].成都:四川师范大学,2012.
[22] 熊涛.由模类Fn决定的同调理论[D].成都:四川师范大学,2015.
[23] ENOCHS E E, HUANG Z Y.Injective envelopes and(Gorenstein)flat covers[J].Algebras and Representation Theory,2012,15(6):1131-1145.
[24] LEE S B.Weak-injective modules[J].Commun Algebra,2006,34(1):361-370.
[25] FUCHS L, SALCE L.Modules over non-noetherian domains[J].American Mathematical Society,2001,84(4):613.

备注/Memo

备注/Memo:
收稿日期:2017-09-02 接受日期:2017-11-07
基金项目:国家自然科学基金(11171240)
*通信作者简介:王芳贵(1955—),男,教授,主要从事交换代数与同调代数的研究,E-mail:wangfg2004@163.com
更新日期/Last Update: 2018-04-15