共查询到20条相似文献,搜索用时 46 毫秒
1.
Wolfram Bauer 《Mathematische Nachrichten》2008,281(6):764-785
Let E be a 𝒟ℱ𝒩‐space and let U ⊂ E be open. By applying the nuclearity of the Fréchet space ℋ︁(U) of holomorphic functions on U we show that there are finite measures μ on U leading to Bergman spaces of μ ‐square integrable holomorphic functions. We give an explicit construction for μ by using infinite dimensional Gaussian measures. Moreover, we prove boundary estimates for the corresponding Bergman kernels Kμ on the diagonal and we give an application of our results to liftings of μ ‐square integrable Banach space valued holomorphic functions over U. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
2.
We consider R‐torsionfree modules over group rings RG, where R is a Dedekind domain and G is a finite group. We compare the (first order) theory T of al these modules and the theory T0 of the finitely generated ones (so of RG‐lattices). It is easy to realize that they are equal iff R is a field. The obstruction is the existence of R‐divisible R‐torsionfree RG‐modules. Accordingly we consider R‐reduced R‐torsionfree RG‐modules for a local R. We show that the key conditions ensuring that their theory equals T0 are: (1) RG‐lattices have a finite representation type; (2) each attice over the completion R̂G is isomorphic to the completion of some RG‐lattice.Some related questions are discussed. 相似文献
3.
Ying-Ying Feng 《代数通讯》2013,41(4):1449-1465
4.
Grace Piper 《Mathematical Logic Quarterly》2009,55(5):562-568
We develop the theory of Cκ, λi, a strongly normal filter over ??κ λ for Mahlo κ. We prove a minimality result, showing that any strongly normal filter containing {x ∈ ??κ λ: |x | = |x ∩ κ | and |x | is inaccessible} also contains Cκ, λi. We also show that functions can be used to obtain a basis for Cκ, λi (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
5.
Ken‐ichi Kawarabayashi 《Journal of Graph Theory》2002,39(2):111-128
Let G be a graph of order 4k and let δ(G) denote the minimum degree of G. Let F be a given connected graph. Suppose that |V(G)| is a multiple of |V(F)|. A spanning subgraph of G is called an F‐factor if its components are all isomorphic to F. In this paper, we prove that if δ(G)≥5/2k, then G contains a K4?‐factor (K4? is the graph obtained from K4 by deleting just one edge). The condition on the minimum degree is best possible in a sense. In addition, the proof can be made algorithmic. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 111–128, 2002 相似文献
6.
Let R be a ring and 𝒲 a self-orthogonal class of left R-modules which is closed under finite direct sums and direct summands. A complex C of left R-modules is called a 𝒲-complex if it is exact with each cycle Z n (C) ∈ 𝒲. The class of such complexes is denoted by 𝒞𝒲. A complex C is called completely 𝒲-resolved if there exists an exact sequence of complexes D · = … → D ?1 → D 0 → D 1 → … with each term D i in 𝒞𝒲 such that C = ker(D 0 → D 1) and D · is both Hom(𝒞𝒲, ?) and Hom(?, 𝒞𝒲) exact. In this article, we show that C = … → C ?1 → C 0 → C 1 → … is a completely 𝒲-resolved complex if and only if C n is a completely 𝒲-resolved module for all n ∈ ?. Some known results are obtained as corollaries. 相似文献
7.
Let 𝔉 be a class of groups and G a finite group. A maximal subgroup M of G is called 𝔉-abnormal provided G∕MG?𝔉. Let K<H be subgroup of G. Then we say that (K,H) is an 𝔉-abnormal pair of G provided K is a maximal 𝔉-abnormal subgroup of H. Let A be a subgroup of G. Then we say that A is 𝔉-quasipermutable in G provided A either covers or avoids every 𝔉-abnormal pair of G. In this paper, we consider some applications of 𝔉-quasipermutable subgroups. 相似文献
8.
Fatemeh Zareh-Khoshchehreh 《代数通讯》2018,46(5):2171-2178
Let R be an associative ring with identity. For a given class 𝒮 of finitely presented left (respectively right) R-modules containing R, we present a complete characterization of 𝒮-pure injective modules and 𝒮-pure flat modules. Consider that 𝒮 is a class of (R,R)-bimodules containing R with the following property: every element of 𝒮 is a finitely presented left and right R-module. We give a necessary and sufficient condition for 𝒮 to have Lazard’s theorem, and then we present our desired Lazard’s theorem. 相似文献
9.
We prove the following result: Theorem. Let K be a countable Hilbertian field, S a finite set of local primes of K, and e ≥ 0 an integer. Then, for almost all σ ∈ G (K)e, the field Ks [ σ ] ∩ Ktot,S is PSC. Here a local prime is an equivalent class 𝔭 of absolute values of K whose completion is a local field, 𝔭. Then K𝔭 = Ks ∩ 𝔭 and Ktot,S = ∩𝔭 ∈ S∩σ ∈ G(K) Kσ𝔭. G(K) stands for the absolute Galois group of K. For each σ = (σ1, …, σe ) ∈ G(K)e we denote the fixed field of σ1, …, σe in Ks by Ks( σ ). The maximal Galois extension of K in Ks( σ ) is Ks[ σ ]. Finally “almost all” means “for all but a set of Haar measure zero”. 相似文献
10.
《代数通讯》2013,41(12):4741-4752
Abstract Subgroups A and B of a finite group are said to be 𝒩-connected if the subgroup generated by elements x and y is a nilpotent group, for every pair of elements x in A and y in B. The behaviour of finite pairwise permutable and 𝒩-connected products are studied with respect to certain classes of groups including those groups where all the subnormal subgroups permute with all the maximal subgroups, the so-called SM-groups, and also the class of soluble groups where all the subnormal subgroups permute with all the Carter subgroups, the so-called C-groups. 相似文献
11.
We derive decomposition theorems for P6, K1 + P4‐free graphs, P5, K1 + P4‐free graphs and P5, K1 + C4‐free graphs, and deduce linear χ‐binding functions for these classes of graphs (here, Pn (Cn) denotes the path (cycle) on n vertices and K1 + G denotes the graph obtained from G by adding a new vertex and joining it with every vertex of G). Using the same techniques, we also obtain an optimal χ‐binding function for P5, C4‐free graphs which is an improvement over that given in [J. L. Fouquet, V. Giakoumakis, F. Maire, and H. Thuillier, 11 , Discrete Math, 146, 33–44.]. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 293–306, 2007 相似文献
12.
In this article, we settle a problem which originated in 4 regarding the existence of resolvable (K4 ? e)‐design. We solve the problem with two possible exceptions. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 502–510, 2007 相似文献
13.
14.
Leila Goudarzi 《代数通讯》2017,45(9):4093-4098
Let L be a finite dimensional Lie algebra. Then for a maximal subalgebra M of L, a 𝜃-completion for M is a subalgebra C of L such that CM and ML?C and C∕ML contains no non-zero ideal of L∕ML, properly. And a 𝜃-completion C of M is said to be a strong 𝜃-completion, if C = L or there exists a subalgebra B of L such that C be maximal in B and B is not a 𝜃-completion for M. These are analogous to the concepts of 𝜃-completion and strong 𝜃-completion of a maximal subgroup of a finite group. Now, we consider the influence of these concepts on the structure of a finite dimensional Lie algebra. 相似文献
15.
Let v, k be positive integers and k ≥ 3, then Kk = : {v: v ≥ k} is a 3‐BD closed set. Two finite generating sets of 3‐BD closed sets K4 and K5 are obtained by H. Hanani [5] and Qiurong Wu [12] respectively. In this article we show that if v ≥ 6, then v ∈ B3(K,1), where K = {6,7,…,41,45,46,47,51,52,53,83,84}\{22,26}; that is, we show that K is a generating set for K6. Finally we show that v ∈ B3(6,20) for all v ∈ K\{35,39,40,45}. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 128–136, 2008 相似文献
16.
Apoorva Khare 《代数通讯》2013,41(12):4431-4475
This article aims to contribute to the study of algebras with triangular decomposition over a Hopf algebra, as well as the BGG Category 𝒪. We study functorial properties of 𝒪 across various setups. The first setup is over a skew group ring, involving a finite group Γ acting on a regular triangular algebra A. We develop Clifford theory for A?Γ, and obtain results on block decomposition, complete reducibility, and enough projectives. 𝒪 is shown to be a highest weight category when A satisfies one of the “Conditions (S);” the BGG Reciprocity formula is slightly different because the duality functor need not preserve each simple module. Next, we turn to tensor products of such skew group rings; such a product is also a skew group ring. We are thus able to relate four different types of Categories 𝒪; more precisely, we list several conditions, each of which is equivalent in any one setup, to any other setup, and which yield information about 𝒪. 相似文献
17.
Bernhard K?ck 《K-Theory》1991,5(2):177-187
For any finite groupG, which is a split extension with a nilpotent group, we prove a splitting formula forK
q([G]). Applying it to the group of upper (3×3)-matrices over a finite field, we obtain the formula conjectured by Hambleton, Taylor and Williams. 相似文献
18.
Konrad Neumann 《Israel Journal of Mathematics》1998,104(1):221-260
A fieldK is called stable if every finitely generaed regular field extensionF/K has a transcendence basex
1, …,x
n
with the following properties: The field extensionF/K(x
1,…,x
n
) is separable and the Galois hull
ofF/K(x
1,…,x
n
) remains regular overK, i.e.K is algebraically closed in
. We prove in this paper thatevery field is stable. This generalizes results from [FJ1] and [GJ] which prove that fields of characteristic 0 and infinite perfect fields are
stable, respectively. [G] showed that finite fields are stable in dimension 1, i.e. every finitely generated regular field
extension of transcendence degree 1 over a finite field has a stable transcendence base. In the last section of this paper
we apply the theorem to the construction of PAC fields with additional properties. A fieldK is called PAC if every absolutely irreducible variety overK has at least oneK-rational point. 相似文献
19.
Let 𝒜 be an abelian category. A subcategory 𝒳 of 𝒜 is called coresolving if 𝒳 is closed under extensions and cokernels of monomorphisms and contains all injective objects of 𝒜. In this paper, we introduce and study Gorenstein coresolving categories, which unify the following notions: Gorenstein injective modules [8], Gorenstein FP-injective modules [20], Gorenstein AC-injective modules [3], and so on. Then we define a resolution dimension relative to the Gorenstein coresolving category 𝒢?𝒳(𝒜). We investigate the properties of the homological dimension and unify some important properties possessed by some known homological dimensions. In addition, we study stability of the Gorenstein coresolving category 𝒢?𝒳(𝒜) and apply the obtained properties to special subcategories and in particular to module categories. 相似文献
20.
A function between graphs is k‐to‐1 if each point in the codomain has precisely k pre‐images in the domain. Given two graphs, G and H, and an integer k≥1, and considering G and H as subsets of ?3, there may or may not be a k‐to‐1 continuous function (i.e. a k‐to‐1 map in the usual topological sense) from G onto H. In this paper we consider graphs G and H whose order is of a different parity and determine the even and odd values of k for which there exists a k‐to‐1 map from G onto H. We first consider k‐to‐1 maps from K2r onto K2s+1 and prove that for 1≤r≤s, (r, s)≠(1, 1), there is a continuous k‐to‐1 map for k even if and only if k≥2s and for k odd if and only if k≥?s?o (where ?s?o indicates the next odd integer greater than or equal to s). We then consider k‐to‐1 maps from K2s+1 onto K2s. We show that for 1≤r<s, such a map exists for even values of k if and only if k≥2s. We also prove that whatever the values of r and s are, no such k‐to‐1 map exists for odd values of k. To conclude, we give all triples (n, k, m) for which there is a k‐to‐1 map from Kn onto Km in the case when n≤m. © 2009 Wiley Periodicals, Inc. J Graph Theory 65: 35–60, 2010. 相似文献