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1.
设S和R是环.本文证明了若下述条件之一成立,则S和R具有相同的凝聚维数:(1)S是R的优越扩张;(2)S和MMorita等价.作为上述结果的推论,我们证明了环R和下述环类具有相同的凝聚维数:(i)R上的矩阵环Mn(R);(i)R和有限群G(要求|G|-1∈R)的斜群环;(ii)Smash积R#G*(要求G是有限群且|G|-1∈R,R是G分次环)  相似文献   

2.
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   

3.
本文用模的自同态,给出弱总体维数≤n的环的特征,其中n≥0.设R为环,部分地回答了下列问题:何时任意有限表现R-模M有无穷分解:0→M→F0→F1→…→Fn→…,其中每个Fi均是有限生成投射的,i=1,2,…?  相似文献   

4.
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   

5.
王捍贫 《数学进展》1999,28(3):241-251
本文讨论了将分式环S^-1R上的模归约为R上模时noforking性质的保持性,证明了:Ls^-1R中型q是p的noforking扩充当且仅当它们在LR上的限制qR的一个oforking扩充,还讨论了分式模S^-1M与M的oforking性质保持的条件。  相似文献   

6.
关于SF-环的几点注记   总被引:3,自引:0,他引:3  
本文中,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满足特殊右零化于降链条件;(3)R是左SF-环和I-环,且R ̄R具有有限Goldie维数。Ⅱ对于环R,下面条件是等价的:(1)R是VonNeumann正则环;(2)R是左SF-环,且每个苛异循环左R-模的极大子模是平坦的。  相似文献   

7.
关于SF—环的几点注记   总被引:1,自引:0,他引:1  
章聚乐 《数学杂志》1994,14(2):197-202
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   

8.
广义自相似集的维数研究   总被引:8,自引:0,他引:8  
华苏 《应用数学学报》1994,17(4):551-558
广义自相似集的维数研究华苏(清华大学应用数学系,北京100084)ONTHEDIMENSIONOFGENERALIZEDSELR-SIMILARSETS¥HUASU(DepartmentofAppliedMathematics,TsinghuaUni...  相似文献   

9.
关于McCoy定理章聚乐,杜先能(安徽师范大学数学系,芜湖)关键词素理想,m-系,*-素子模,对偶模.分类号^。S(1991)16D3。/cC。。153.3本文中,R表示有单位元的结合环,M表示左R一模,并且M的对偶模Horn。(M,R)记为M”.模...  相似文献   

10.
GCD整环与自反模   总被引:3,自引:0,他引:3  
本文证明了凝聚整环是GCD整环当且仅当秩为1的自反模是自由模.同时还得到有限弱整体维数的凝聚整环是GCD整环当且仅当Pic(R)=1.特别地,有限整体维数的Noether整环是UFD当且仅当Pic(R)=1.  相似文献   

11.
卢博 《数学季刊》2012,(1):128-132
Let R be a noetherian ring and S an excellent extension of R.cid(M) denotes the copure injective dimension of M and cfd(M) denotes the copure flat dimension of M.We prove that if M S is a right S-module then cid(M S)=cid(M R) and if S M is a left S-module then cfd(S M)=cfd(R M).Moreover,cid-D(S)=cid-D(R) and cfd-D(S)=cfdD(R).  相似文献   

12.
In this paper conditions on the commutative ring R (with identity) and the commutative semigroup ring S (with identity) are found which characterize those semigroup rings R[S] which are reduced or have weak global dimension at most one. Likewise, those semigroup rings R[S] which are semihereditary are completely determined in terms of R and S.  相似文献   

13.
Let R be a commutative coherent ring and wD(R) denote the weak global dimension of R.We prove that for an integer n≥2 the following are equivalent:.

(a) wD(R)n;.

(b) FP-idM ?Gn-2 for all (FP-)injectives G and for all modules M;.

(c) fdHom(G,M)n-2 for all (FP-)injectives G and for all modules M;.

(d) fdHom(M,G)n-2 for all flat modules G and for all modules M.  相似文献   

14.
Let R be a left coherent ring, FP — idRR the FP — injective dimension of RR and wD(R) the weak global dimension of R. It is shown that 1) FP -idRR < n ( n > 0) if and only if every flat resolvent 0 → M → F° → F1... of a finitely presented right R—module M is exact at F'(i > n?1) if and only if every nth F -cosyzygy of a finitely presented right R — module has a flat preenvelope which is a monomorphism; 2) wD(R) < n (n > 1) if and only if every (n?l)th F-cosyzygy of a finitely presented right R—module has a flat preenvelope which is an epimorphism; 3) wD(R) 0) if and only if every nth F — cosyzygy of a finitely presented right R — module is flat. In particular, left FC rings and left semihereditary rings are characterized  相似文献   

15.
In this paper, we present the results of a study of real-world applications of O.R./M.S. as seen in journals. Five leading journals in the field are surveyed, and real-world application articles are classified using a two dimensional framework consisting of orientation and decision. The orientation dimension separates strategically oriented applications with long-term implications and tactically oriented applications with medium- and short-term implications. The decision dimension refers to the type of decision in the application-largely structured or largely unstructured. The major O.R./M.S. topics are placed in the resulting four quadrants, and articles published in the four most recent volumes of the five journals are classified. Based on the results of this survey, the thrust and shortcomings of implementation research are discussed. Some measures for enhancing publication of field-based research are also proposed.  相似文献   

16.
It is proved that if a PI-ring R has a faithful left R-module M with Krull dimension, then its prime radical rad(R) is nilpotent. If, moreover, the R-module M and the left idealR(rad(R)) are finitely generated, then R has a left Krull dimension equal to the Krull dimension of M. It turns out that a semiprime ring, which has a faithful (left or right) module with Krull dimension, is a finite subdirect product of prime rings. Moreover, first, a right Artinian ring R such that rad(R)2=0 has a faithful Artinian cyclic left module, and second, a finitely generated semiprime PI-algebra over a field has a faithful Artinian module. We give examples showing that the restrictions imposed are essential, as well as an example of a finitely generated prime PI-algebra over a field, which is not Noetherian and has a Krull dimension. Supported by RFFR grant No. 26-93-011-1544. Translated fromAlgebra i Logika, Vol. 36, No. 5, pp. 562–572, September–October, 1997.  相似文献   

17.
In this paper we study the link between formal group of dimension one and integrable derivations of a ring of unequal characteristic. Partially supported by M.U.R.S.T. (60%) and members of C.N.R.-G.N.S.A.G.A.  相似文献   

18.
任伟 《数学学报》2019,62(4):647-652
设R■A是环的Frobenius扩张,其中A是右凝聚环,M是任意左A-模.首先证明了_AM是Gorenstein平坦模当且仅当M作为左R-模也是Gorenstein平坦模.其次,证明了Nakayama和Tsuzuku关于平坦维数沿着Frobenius扩张的传递性定理的"Gorenstein版本":若_AM具有有限Gorenstein平坦维数,则Gfd_A(M)=Gfd_R(M).此外,证明了若R■S是可分Frobenius扩张,则任意A-模(不一定具有有限Gorenstein平坦维数),其Gorenstein平坦维数沿着该环扩张是不变的.  相似文献   

19.
弱半局部环的同调性质   总被引:1,自引:0,他引:1  
环R称为弱半局部环,如果R/J(R)是Von Neumann正则环.给出了一个交换环是弱半局部环的充分且必要条件;还讨论了交换凝聚弱半局部环及其模的同调维数.  相似文献   

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