首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 15 毫秒
1.
The purpose of this paper is to answer an open problem proposed by Matlis on modules with the finite exchange property. The problem is: Let {M i | iI} be an indexed family of indecomposable injective modules and M a direct sum of M i , i.e. M = ⊕{M i | iI} and N a summand of M. Is N a direct sum of indecomposable injective modules, i.e. N = ⊕{M j |jJ, J ? I}? The answer to this problem is affirmative for module M with finite exchange property.  相似文献   

2.
Bui Xuan  Hai  Cao Minh  Nam  Mai Hoang  Bien 《Mathematical Notes》2020,108(5-6):769-774
Mathematical Notes - In this note, we study the problem on the existence of noncyclic free subgroups of the skew group algebra of a locally finite group over a field.  相似文献   

3.
It is shown that the variety generated by a finite modular lattice has only finitely many locally finite covers.   相似文献   

4.
We give a new, geometric proof of a theorem by Timmesfeld showing that for simple Chevalley groups, abstract modules where all roots act quadratically are direct sums of minuscule representations. Our proof is uniform, treats finite and infinite fields on an equal footing, and includes Lie rings.  相似文献   

5.
6.
We show that given an affine algebraic group G over a fieldK and a finite subgroup scheme H of G there exists a finitedimensional G-module V such that V|H is free. The problem israised in the recent paper by Kuzucuglu and Zalesski [15] which containsa treatment of the special case in which K is the algebraicclosure of a finite field and H is reduced. Our treatment isdivided into two parts, according to whether K has zero or positivecharacteristic. The essence of the characteristic 0 case isa proof that, for given n, there exists a polynomial GLn(Q)-moduleV of dimension , where the product is over all primes less than or equal to n+1, such thatV is free as a QH-module for every finite subgroup H of GLn(Q).The module V is the tensor product of the exterior algebra *(E),on the natural GLn(Q)-module E, and Steinberg modules Stp, onefor each prime not exceeding n+1. The Steinberg modules alsoplay the major role in the case in which K has characteristicp>0 and the key point in our treatment is to show that fora finite subgroup scheme H of a general linear group scheme(or universal Chevalley group scheme) G over K, the Steinbergmodule Stpn for G is injective (and projective) on restrictionto H for n>>0. A curious consequence of this is that,despite the wild behaviour of the modular representation theoryof finite groups, one has the following. Let H be a finite groupand V a finite dimensional vector space. Then there exists a(well-understood) faithful rational representation GL(V)GL(W)such that, for each faithful representation : HGL(V), the compositeo: HGL(W) is free, in particular all representations o are equivalent.  相似文献   

7.
In this paper we study Auslander-Reiten sequences of modules with finite complexity over selfinjective artin algebras. In particular, we show that for all eventually Ω-perfect modules of finite complexity, the number of indecomposable non projective summands of the middle term of such sequences is bounded by 4. We also describe situations in which all non projective modules in a connected component of the Auslander-Reiten quiver are eventually Ω-perfect.  相似文献   

8.
We show that for an arbitrary logic being locally tabular is a strictly weaker property than being locally finite. We describe our hunt for a logic that allows us to separate the two properties, revealing weaker and weaker conditions under which they must coincide, and showing how they are intertwined. We single out several classes of logics where the two notions coincide, including logics that are determined by a finite set of finite matrices, selfextensional logics, algebraizable and equivalential logics. Furthermore, we identify a closure property on models of a logic that, in the presence of local tabularity, is equivalent to local finiteness.  相似文献   

9.
Let R be a commutative Noetherian ring, and let N be a non-zero finitely generated R-module. The purpose of this paper is to show that N is locally unmixed if and only if, for any N-proper ideal I of R generated by ht N I elements, the topology defined by (I N)(n), n ≥ 0, is linearly equivalent to the I-adic topology.  相似文献   

10.
11.
Sozutov  A. I. 《Mathematical Notes》2001,69(5-6):833-838
A proper subgroup H of a group G is said to be strongly isolated if it contains the centralizer of any nonidentity element of H and 2-isolated if the conditions >C G(g) H 1 and 2(CG(g)) imply that CG(g)H. An involution i in a group G is said to be finite if |ii g| < (for any g G). In the paper we study a group G with finite involution i and with a 2-isolated locally finite subgroup H containing an involution. It is proved that at least one of the following assertions holds:1) all 2-elements of the group G belong to H;2) (G,H) is a Frobenius pair, H coincides with the centralizer of the only involution in H, and all involutions in G are conjugate;3) G=FFCG(i) is a locally finite Frobenius group with Abelian kernel F;4) H=V D is a Frobenius group with locally cyclic noninvariant factor D and a strongly isolated kernel V, U=O2(V) is a Sylow 2-subgroup of the group G, and G is a Z-group of permutations of the set =U g g G.  相似文献   

12.
13.
Infinite transitive permutation groups all proper subgroups of which have just finite orbits are treated. Under the extra condition of being locally finite, such groups are proved to be primary, and, moreover, soluble if the stabilizer of some point is soluble.  相似文献   

14.
Let (R, 𝔪) be a commutative Noetherian local ring. It is known that R is Cohen–Macaulay if there exists either a nonzero finitely generated R-module of finite injective dimension or a nonzero Cohen–Macaulay R-module of finite projective dimension. In this article, we investigate the Gorenstein analogues of these facts.  相似文献   

15.
16.
局部可数集族、局部有限集族与Alexandroff问题   总被引:9,自引:0,他引:9  
本文引进分层强s-映射和分层强紧映射建立具有σ-局部可数网、具有σ-局部可数k-网、具有σ-局部可数基的正则空间以及σ-空间、-空间、g-可度量空间和确定的度量空间之间的联系.这些都是对Alexandroff问题的回答.  相似文献   

17.
Xiangyu Feng 《代数通讯》2013,41(5):1700-1708
Let R be a ring and R ω a self-orthogonal module. We introduce the notion of the right orthogonal dimension (relative to R ω) of modules. We give a criterion for computing this relative right orthogonal dimension of modules. For a left coherent and semilocal ring R and a finitely presented self-orthogonal module R ω, we show that the projective dimension of R ω and the right orthogonal dimension (relative to R ω) of R/J are identical, where J is the Jacobson radical of R. As a consequence, we get that R ω has finite projective dimension if and only if every left (finitely presented) R-module has finite right orthogonal dimension (relative to R ω). If ω is a tilting module, we then prove that a left R-module has finite right orthogonal dimension (relative to R ω) if and only if it has a special ω-preenvelope.  相似文献   

18.
19.
Siberian Mathematical Journal - Let&nbsp; $ {mathfrak{M}} $ be a&nbsp;set of finite groups. Given a&nbsp;group&nbsp; $ G $ , denote the set of all subgroups of&nbsp; $ G $...  相似文献   

20.
The subject of this paper are infinite, locally finite, vertex-transitive median graphs. It is shown that the finiteness of the Θ-classes of such graphs does not guarantee finite blocks. Blocks become finite if, in addition, no finite sequence of Θ-contractions produces new cut-vertices. It is proved that there are only finitely many vertex-transitive median graphs of given finite degree with finite blocks. An infinite family of vertex-transitive median graphs with finite intransitive blocks is also constructed and the list of vertex-transitive median graphs of degree four is presented. Sandi Klavžar: Supported by the Ministry of Science of Slovenia under the grant P1-0297. The author is also with the Faculty of Mathematics and Natural Sciences, University of Maribor, Slovenia and the Institute of Mathematics, Physics and Mechanics, Ljubljana.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号