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1.
一类环上HX环的结构 总被引:11,自引:2,他引:9
自李洪兴1991年提出了HX环以来,人们一直有这么一个问题没解决,就是是否存在非平凡的HX环的例子?但至今既没找到非平凡的HX环,也没有证明任一环R仅存在平凡的HX环。针对这个问题,本文提出并证明了一类环仅有平凡HX环,还给出了一系列的结构定理。这样,既为证明任一环R仅有平凡的HX环的猜想有新的启示,也为人们指明无须在这一类环上寻找非平凡HX环。 相似文献
2.
本文研究了一般半群环的右Artin性的刻划问题,改进了JanOkniski在[3]中的结果,并给出了半群环是右Artin环的刻划.最后进一步指出在一定条件下,R[S1]和R[S1]的链条件是等价的. 相似文献
3.
广义幂级数环的拟Baer性 总被引:3,自引:0,他引:3
设R是环,(S,≤)是严格全序幺半群,且对任意s∈S都有0≤s.本文证明了环R是拟Baer环当且仅当R上的广义幂级数环[RS,≤]]是拟Baer环。 相似文献
4.
刘仲奎 《数学年刊A辑(中文版)》2002,(5)
设R是环,(S,≤)是严格全序幺半群,且对任意s∈S都有0≤s.本文证明了环R是拟Baer环当且仅当R上的广义幂级数环[[RS,≤]]是拟 Baer环. 相似文献
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6.
本文引进了分次环的分次Excellent扩张概念,设S=⊕_(g∈G)S_g是R=⊕_(g∈G)R_g的分次Excellent扩张,证明了S是分次右V-环当且仅当R是分次右V-环,S是分次PS-环当且仅当R是分次PS-环,S是分次Von Neumann正则环当且仅当R是分次Von Neumann正则环。 相似文献
7.
设R′是一个环,Mn′(R′)是R′上的n′×n′矩阵环.如果环R有不变基数性质并且每个有限生成的投射左R-模是自由模,则R是一个投射自由环.如果环R≌Mr(S),其中S是一个投射自由环,则R是一个投射可迁环.当R是一个投射可迁环时,给出了从Mn′(R′)到Mn(R)(n′≥n≥2)的若当同态的代数公式. 相似文献
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本文得到:具有细链双曲无穷远鞍点和一个细焦点的二次系统至多存在一个极限环,若有细无穷远分界线环S,则其内部不存在极限环,其稳定性与它包围的奇点的稳定性相反. 相似文献
10.
杜先能 《数学年刊A辑(中文版)》2006,(2)
本文研究形式三角矩阵环 R 的若干新性质,讨论 R-模的伪投射性,给出了形式三角矩阵环 R 是 V-环或半 V-环的充要条件.同时,给出了 R 是 PS-环的条件. 相似文献
11.
设R是含幺结合环,Pg(R)是R的所有投射生成元的同构类组成的半群,Gr(Pg(R))是Pg(R)的Grothendieck群,在本文中我们证明了K0(R)=Gr(Pg(R))。由此我们得到对任意VBN环R,存在环S满足S^2=S并且具有Aut-Pic性质,最后我们给出了环的一个分类,并且用Pg(R)的周期性对它作了描述。 相似文献
12.
A ring of quotients of the semigroup ring R(S) is discussed where R has a σ-set Σ and S has a σ-set Δ. In particular, we study
the cases where (1) R is an integral domain and S is a commutative cancellative semigroup, (2) R is a commutative ring and
S is a semilattice and (3) R is a commutative ring and S is a Rees matrix semigroup over a semigroup.
Communicated by G. Lallement 相似文献
13.
Excellent Extensions of RingsLiuZhongkui(刘仲奎)andWangTingZhen(王廷桢)(DepartmentofMathcmatics,NorthwestNormalUniversity,Lanzhon,7... 相似文献
15.
Zuo Lancui 《大学数学》1998,(1)
本文研究了所有R—投射模都是投射模的环(RP—环),得出了它的几个等价条件,证明了:S=Rn为RP—环当且仅当R为RP—环;∑ni=1Ri为RP—环当且仅当每个Ri为RP—环.讨论了RP—环的左投射维数. 相似文献
17.
<正> 熟知地,满足极小条件的单纯环只与一个有限维向量空间的线性变换的完全环同构.并且此向量空间如取为左向量空间的话,那末R的任一极小右理想均可取为此左向量空间.在没有有限条件情况下,Jacobsoo用本原环来取代这种单纯环.接着Wolfson研 相似文献
18.
This paper is concerned with the question of when a Schmidt differential operator ring S over a ring R must have the same uniform rank or reduced rank as R. Also, some information about those prime ideals of R which are invariant under a Schmidt higher derivation is derived. All rings in this paper are associative with unit and all modules are unital right modules. In [1], Bell and Goodearl proved that for a Poincaré-Birkhoff-Witt extension T of a ring R, the rank of T and the rank of R agree when R is a right noetherian ring with no Z-torsion which is tame as a right module over itself. In this paper, we show that for a Schmidt differential operator ring S over a right noetherian ring R with no Z-torsion which is tame as a right module over itself the rank of S and the rank of R agree. Also, for any right noetherian R, it is proved that RR and SS have the same reduced rank. 相似文献
19.
Günter Törner 《Journal of Geometry》1974,5(1):1-13
The main result of this paper is a representation theorem for incidence morphisms of desarguesian Hjelmslev planes which preserve basis quadrangles. We prove that each geometric morphism between desarguesian Hjelmslev planes (R), (S) induces a total order of the coordinate ring R and a partial homomorphism from R to S. Conversely we have for each partial homomorphism and every partial order a uniquely determined geometric morphism. By a total order A of a ring R we mean a subring of R such that the elements of R/A are units in R, with inverses lying in A. If we have such a total order A \( \subseteq \) R, a partial homomorphism from R to another ring S is essentially a homomorphism from A to S. 相似文献