共查询到19条相似文献,搜索用时 171 毫秒
1.
本文证明了如下结果:环R是Artin半单的当且仅当存在一个基数c,使得任意左R-模是一个连续模和一个c-限制的ES-模的直和,也当且仅当存在一个基数c,使得任意左界R-模是一个拟投射模和一个c-限制的ES-模的直和。 相似文献
2.
关于局部Noether模 总被引:2,自引:0,他引:2
本文证明了如下结果:左 R-模 M是局部 Noether模当且仅当σ[M]中的任意M-内射左R-模的直和是一个有限余生成左R-模和一个拟连续(或连续,直内射)左R-模的直和. 相似文献
3.
主左理想由若干个幂等元生成的环 总被引:1,自引:0,他引:1
环R称为左PI-环,是指R的每个主左理想由有限个幂等元生成.本文的主要目的是研究左PI-环的von Neumann正则性,证明了如下主要结果:(1)环R是Artin半单的当且仅当R是正交有限的左PI-环;(2)环R是强正则的当且仅当R是左PI-环,且对于R的每个素理想P,R/P是除环;(3)环R是正则的且R的每个左本原商环是Artin的当且仅当R是左PI-环且R的每个左本原商环是Artin的;(4)环R是左自内射正则环且Soc(RR)≠0当且仅当R是左PI-环且它包含内射极大左理想;(5)环R是MELT正则环当且仅当R是MELT左PI-环. 相似文献
4.
关于半交换环与强正则环 总被引:1,自引:0,他引:1
本文得到了环R是强正则环的若干充分必要条件,证明了下面条件是等价的:(1)R是强正则的;(2)R是半交换正则的;(3)R是半交换的左SF-环;(4)R是半交换的ELT环,且使得每个单左R-模是P-内射的或者平坦的;(5)R是半交换右非奇异的左SF-环;(6)R是半素的半交换左(或右)P-内射环. 相似文献
5.
REMARKS ON QUASI-PERFECT RINGS AND FC-RINGS 总被引:1,自引:0,他引:1
设R是有单位元的环,S是R的几乎优越扩张,G是有限群且|G|-1∈R.证明了R是FC-环(拟完备环,凝聚环)当且仅当S是FC-环(拟完备环,凝聚环),也当且仅当Smach积R#G*是FC-环(拟完备环,凝聚环). 相似文献
6.
作为幂级数环的推广,Ribenboim引入了广义幂级数环的概念.设R是有单位元的交换环,(J,≤)是严格全序半群.本文中我们证明了如下结果:(1)广义幂级数环 [[Rs]]是PP-环当且仅当R是PP-环且B(R)的任意 S-可标子集C在B(R)中有最小上界;(2)如果对任意s∈S都有0≤s,则[[Rs,≤]]是弱PP-环当且仅当R是弱PP-环.我们还给出了一个例子说明交换的弱PP-环可以不是PP-环. 相似文献
7.
Artin模的自同态环 总被引:1,自引:0,他引:1
武同锁 《数学年刊A辑(中文版)》1995,(2)
本文讨论Artin模的自同态环何时为半完全环的问题.对于Artin模MR,本文证明了:(1)若M是非单的直和不可分解模,则socM为见的小子模;(2)对任意Artin模M及任意Artin半单模L,EndR(ML)为半完全环的充要条件为EndR(M)是半完全环.本文还证明了(直和不可分解的)拟投射Artin模的自同态环为(局部环)半准素环.而对于非零的Artin投射模P,“P直和不可分解”等价于“P和不可分解”. 相似文献
8.
本文中讨论了一类比半局部环更广的环类,即G-半局部环,对G-半局部我们通过模去环的左Soche及Jacobson根,研究了环的同调维数,并得到Gd(R/S)=Gd(R/S∩J),式中的Gd表示环R的左整体维数或右整体维数,S=Soc(R^R)以及J是环R的Jacobson根,当R还时半本原环时,即得Gd(R/S)=Gd(R)。 相似文献
9.
关于SF—环的几点注记 总被引:1,自引:0,他引:1
文中,我们证明了如下主要结果:Ⅰ对于环R,下面条件是等价的:(1)R是Artin半单环;(2)R是左SF-环,且R满足特殊右零化子降链条件;(3)R是左SF-环和Ⅰ-环,且R^R具有有限Goldie维数。Ⅱ对于环R,下面条件是等价:(1)R是Von Neumann正则环;(2)R是左SF-环,且每个奇异循环左R-模的极大子模是平坦的。 相似文献
10.
文章证明了:如果R或要为本原Artin的Exchange环,则Mn(R)≌(S)当且仅当R≌S。 相似文献
11.
Liu Zhongkui 《东北数学》1994,(3)
OnRightHereditaryRingsandDedekindDomainsLiuZhongkui(刘仲奎)(DepartmentofMathematics,NorthwestNormalUniversity,Lanzhou,730070)Abs... 相似文献
12.
A module M over a ring R is called a lifting module if every submodule A of M contains a direct summand K of M such that A/K is a small submodule of M/K (e.g., local modules are lifting). It is known that a (finite) direct sum of lifting modules need not be lifting. We prove that R is right Noetherian and indecomposable injective right R-modules are hollow if and only if every injective right R-module is a direct sum of lifting modules. We also discuss the case when an infinite direct sum of finitely generated modules containing its radical as a small submodule is lifting. 相似文献
13.
It is proved that a semiperfect module is lifting if and only if it has a projective cover preserving direct summands. Three corollaries are obtained: (1) every cyclic module over a ring R is lifting if and only if every cyclic R-module has a projective cover preserving direct summands; (2) a ring R is artinian serial with Jacobson radical square-zero if and only if every (2-generated) R-module has a projective cover preserving direct summands; (3) a ring R is a right (semi-)perfect ring if and only if (cyclic) lifting R-module has a projective cover preserving direct summands, if and only if every (cyclic) R-module having a projective cover preserving direct summands is lifting. It is also proved that every cyclic module over a ring R is ⊕-supplemented if and only if every cyclic R-module is a direct sum of local modules. Consequently, a ring R is artinian serial if and only if every left and right R-module is a direct sum of local modules. 相似文献
14.
众所周知,环R是右Noether的当且仅当任意内射右R-模的直和是内射的.本文我们将用Ne-内射模和U-内射模来刻画Ne-Noether环和U-Noether环. 相似文献
15.
In this article, we investigate when every simple module has a projective (pre)envelope. It is proven that (1) every simple right R-module has a projective preenvelope if and only if the left annihilator of every maximal right ideal of R is finitely generated; (2) every simple right R-module has an epic projective envelope if and only if R is a right PS ring; (3) Every simple right R-module has a monic projective preenvelope if and only if R is a right Kasch ring and the left annihilator of every maximal right ideal of R is finitely generated. 相似文献
16.
S-内射模及S-内射包络 总被引:1,自引:0,他引:1
设R是环.设S是一个左R-模簇,E是左R-模.若对任何N∈S,有Ext_R~1(N,E)=0,则E称为S-内射模.本文证明了若S是Baer模簇,则关于S-内射模的Baer准则成立;若S是完备模簇,则每个模有S-内射包络;若对任何单模N,Ext_R~1(N,E)=0,则E称为极大性内射模;若R是交换环,且对任何挠模N,Ext_R~1(N,E)=0,则E称为正则性内射模.作为应用,证明了每个模有极大性内射包络.也证明了交换环R是SM环当且仅当T/R的正则性内射包e(T/R)是∑-正则性内射模,其中T=T(R)表示R的完全分式环,当且仅当每一GV-无挠的正则性内射模是∑-正则性内射模. 相似文献
17.
A widely used result of Wedderburn and Artin states that “every left ideal of a ring R is a direct summand of R if and only if R has a unique decomposition as a finite direct product of matrix rings over division rings.” Motivated by this, we call a module M virtually semisimple if every submodule of M is isomorphic to a direct summand of M and M is called completely virtually semisimple if every submodule of M is virtually semisimple. We show that the left R-module R is completely virtually semisimple if and only if R has a unique decomposition as a finite direct product of matrix rings over principal left ideal domains. This shows that R is completely virtually semisimple on both sides if and only if every finitely generated (left and right) R-module is a direct sum of a singular module and a projective virtually semisimple module. The Wedderburn-Artin theorem follows as a corollary from our result. 相似文献
18.
<正> 为了进一步对本原环结构的研究,本文引进规范环的概念,我们说环R是规范的,若R是一个线性变换完全环并且及的基座对于任一对应基{E_i}皆有=∑RE_i=∑E_iR.容易知道,满足单侧理想极小条件的单纯环必是规范的. 相似文献