共查询到20条相似文献,搜索用时 15 毫秒
1.
D. J. Benson 《Algebras and Representation Theory》1999,2(3):287-294
Let k be a commutative ring of coefficients and G be a finite group. Does there exist a flat k G-module which is projective as a k-module but not as a k G-module? We relate this question to the question of existence of a k-module which is flat and periodic but not projective. For either question to have a positive answer, it is at least necessary to have |k| ≥ ?ω. There can be no such example if k is Noetherian of finite Krull dimension, or if k is perfect. 相似文献
2.
Let R be an associative ring with unit, let S be a semigroup with zero, and let RS be a contracted semigroup ring. It is proved that if RS is radical in the sense of Jacobson and if the element 1 has infinite additive order, then S is a locally finite nilsemigroup. Further, for any semigroup S, there is a semigroup T S such that the ring RT is radical in the Brown--McCoy sense. Let S be the semigroup of subwords of the sequence abbabaabbaababbab..., and let F be the two-element field. Then the ring FS is radical in the Brown--McCoy sense and semisimple in the Jacobson sense. 相似文献
3.
4.
In this paper we consider serial rings with T-nilpotent prime radical, factor-rings of which by the prime radical are right Noetherian rings. We prove that the prime quiver
of such a ring is a disconnected union of cycles and chains. In the case when the prime quiver of such a serial ring is a
chain the prime radical is nilpotent. For serial rings with nilpotent prime radical we introduce an analogue of Kupisch series.
Presented by Yu. Drozd
Mathematics Subject Classifications (2000) 16P40, 16G10. 相似文献
5.
设Ω是有限结合环类中全部弱单环组成的环类,Ω1∪Ω2=Ω,Ω1∩Ω2=Φ,在有限结合环类中,我们证明了LΩ1=UΩ2可以成立,并给出等式成立的充要条件.使用这个结论,我们可以证明,在有限结合环类中,超幂零根是特殊根. 相似文献
6.
7.
有限交换环上典型群的Carter子群 总被引:3,自引:0,他引:3
令R为有限交换局部环,K为其剩余类域,令|K|=q.本文研究了R上辛群Sp2nR和正交群O2nR的Carter子群的存在性及结构,并给出R上正交群O2nR在q≡-1(mod 4)情况下的Sylow 2-子群的正确描述. 相似文献
8.
环$R$称为是半clean的, 是指环中的每个元素都是一个单位与一个周期元的和. clean环是半clean的. 刻画半clean群环的一般情形是不容易的. 我们的目的是考虑如下问题:若$G$ 是局部有限群或者是阶是3的循环群, 群环$RG$何时是semiclean的. clean群环上的一些已有结果被推广. 相似文献
9.
René Schoof 《Compositio Mathematica》2001,128(1):1-15
Let R be a local Artin ring with maximal ideal m and residue class field of characteristic p > 0. We show that every finite flat group scheme over R is annihilated by its rank, whenever m
p
= pm = 0. This implies that any finite flat group scheme over an Artin ring the square of whose maximal ideal is zero, is annihilated by its rank. 相似文献
10.
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
11.
Supersemiprime Rings and Supersemiprime Radical 总被引:3,自引:1,他引:3
§1. IntroductionInthisrecentyears,theprimeringswithspecialpropertieshavebeenstudiedsomeau-thors,forexample,N.T.Groenewaldintroducedthecompletelyprimeringsandthecompletelyrimeradicalin[1].D.HandelmanandJ.Lawrencediscussedthestronglyprimeringsandthestronglyprimeradicalin[2].S.Veldsmanstudiedthesuperprimeringsandthesuperprimeradicalin[3].ZhangXianjunintroducedtheAbsolutelysemiprimeringsandtheabsolutelysemiprimeradicalandsoon.Theaimofthispaperistostudythesemiprimeringswithspecialpropertiesan… 相似文献
12.
有限交换环上典型群的Sylow子群 总被引:6,自引:2,他引:4
令R为有限交换局部环,M表其唯一的极大理想,k表其剩余类域.本文定出了R上的一般线性群GLnR,辛群Sp2nR及双曲正交群O2nR的Sylow子群.一般讲,若charx=p,上述三类典型群的Sylow p-子群分别同构于由某些特殊形式的矩阵生成的子群;若chark≠p,上述三类典型群的Sylowp-子群分别同构于一循环群或半二面体群与若干Zp型循环群的圈积。 相似文献
13.
Martin Hertweck 《代数通讯》2013,41(9):3224-3229
It is shown that in the units of augmentation one of an integral group ring ? G of a finite group G, a noncyclic subgroup of order p 2, for some odd prime p, exists only if such a subgroup exists in G. The corresponding statement for p = 2 holds by the Brauer–Suzuki theorem, as recently observed by Kimmerle. 相似文献
14.
O. D. Artemovych 《Periodica Mathematica Hungarica》1998,36(1):1-16
In this paper we study the rings of finite rank which have only trivial derivations (respectively endomorphisms). The main
results are characterizations of these rings.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
16.
将Minkowski关于有限整数矩阵群的著名结果推广到一般的环上,主要结果是证明了:对任意环R,如果R的加法群为有限生成的自由Abel群,则R的所有乘法可逆元构成的群U(R)中的有限子群精确到同构只有有限多个. 相似文献
17.
P. A. Krylov 《Algebra and Logic》2004,43(1):34-43
The Jacobson radical of an endomorphism ring is computed for a completely decomposable torsion-free Abelian group and for a mixed Abelian group in one class of mixed groups. For the latter case, we also look into the question when a factor ring w.r.t. the radical is regular in the sense of Nuemann. 相似文献
18.
WANG XIU-LAN 《东北数学》2012,28(1)
A ring R is called clean if every element is the sum of an idempotent and a unit,and R is called uniquely strongly clean (USC for short) if every element is uniquely the sum of an idempotent and a unit... 相似文献
19.
格序环的一个根的结构 总被引:1,自引:1,他引:1
从不同角度刻画了格序环R的P-根和l-B根,并对l-Q根环进行了讨论.揭示了R及R上的全矩阵环Rn的l-Q根,l-Q理想,素l-理想,半素l-理想之间的关系. 相似文献