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昝立博  陈建龙 《东北数学》2007,23(2):151-156
Let R be an associative ring with identity.R is said to be semilocal if R/J(R)is(semisimple)Artinian,where J(R)denotes the Jacobson radical of R.In this paper,we give necessary and sufficient conditions for the group ring RG to be semilocal,where G is a locally finite nilpotent group.  相似文献
2.
Jér?me Burési 《K-Theory》1995,9(6):551-566
Letk be a field of characteristic different from 2 and ø be a galoisian cohomological class ofk, with values in /2. J. K. Arason proved that ø is killed by a cup-product power of (–1) if and only if the restriction of ø is zero in all the real closedk-extensions. In this paper, we extend such a local-global principle to semilocal rings with 2 a unit, étale cohomology replacing Galois cohomology.  相似文献
3.
赵巨涛  黄寄洪 《数学研究》2004,37(3):292-298
文 [1],[2 ]分别研究了Gr NoetherGr 局部 (半局部 )环的同调维数 ,本文主要进一步讨论Gr 凝聚Gr 半局部环的同调性质 .在§ 1中 ,主要刻画交换Gr 凝聚Gr 半局部环R的分次弱整体维数gr.gl.w .dimR ;在§ 2中 ,定义了分次环R的小有限分次投射维数gr.fp .dimR .刻画了gr.fp .dimR =gr .gl.w .dimR的Gr 凝聚环 .由于Gr Noether环是Gr 凝聚的 ,因而本文所得的结果对于Gr Noether环是自然成立的 .同时 ,本文所得的结果 ,也可视为文 [4 ]关于一般交换凝聚环相应结论的推广 .  相似文献
4.
We study local morphisms in the setting of general noncommutative rings. In particular, we apply local morphisms to study endomorphism rings of modules. We use our constructions to determine classes of modules with semilocal endomorphism rings. For instance, we prove that every finitely presented right module over a semilocal ring has a semilocal endomorphism ring.Alberto Facchini was partially supported by Gruppo Nazionale Strutture Algebriche e Geometriche e loro Applicazioni of Istituto Nazionale di Alta Matematica, Italy, and by Università di Padova (Progetto di Ateneo CDPA048343 “Decomposition and tilting theory in modules, derived and cluster categories”).Dolors Herbera was partially supported by the DGI and the European Regional Development Fund, jointly, through Project BFM2002-01390, and by the Comissionat per Universitats i Recerca of the Generalitat de Catalunya.  相似文献
5.
The aim of this paper is twofold. On the one hand, we show that the dual Goldie dimension codim(End(M R )) of the endomorphism ring End(M R ) of a module M R can be used as a measure of the dimension of the module M R . On the other hand, we prove under suitable hypotheses the validity of the Krull–Schmidt Theorem for infinite direct sums of modules with homogeneous semilocal endomorphism rings.  相似文献
6.
§1. IntroductionThepurposeofthispaperistocomputetheGrothendieckgroupofT=RMNS(θ,φ).TiscalledtheringofMoritaContextinsomeliterature(see[1]).In1974,QuillenannoucedthatK0(RMOS)K0(R)K0(S).UptothepresentmomenttherestillexistsnoinformationconcerningK0(T)f…  相似文献
7.
设R和T是Noether完备半局部环,R→T是环同态.本文证明了,若T是有限生成或ArtinR-模,M为G-Matlis自反R-模,则对所有n≥0,Ext(T,M),Ext(M,T),Tor(T,M)以及Tor(M,T)均是G-Matlis自反T-模.所得结果推广了R.Belshof的结果.  相似文献
8.
给出了可换半局部环的一个外部特征,证明了R为半局部环当且仅当存在可逆R-模,其Top为Artin模.  相似文献
9.
本文中讨论了一类比半局部环更广的环类,即G-半局部我们通过模去环的左Socle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)以及J是环R的Jacobson根。当R还是半本原环时,即得Gd(R/S)=Gd(R)。  相似文献
10.
主要借助small-内射模(环),给出半局部环的正则性和强正则性的一些等价刻画.  相似文献
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