共查询到20条相似文献,搜索用时 31 毫秒
1.
Luchezar L. Avramov Ragnar-Olaf Buchweitz Srikanth Iyengar 《Inventiones Mathematicae》2007,169(1):1-35
A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules
over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class – a substitute
for the length of a free complex – and on the rank of a differential module in terms of invariants of its homology. These
results specialize to basic theorems in commutative algebra and algebraic topology. One instance is a common generalization
of the equicharacteristic case of the New Intersection Theorem of Hochster, Peskine, P. Roberts, and Szpiro, concerning complexes
over commutative noetherian rings, and of a theorem of G. Carlsson on differential graded modules over graded polynomial rings. 相似文献
2.
A. Yu. Golubkov 《Journal of Mathematical Sciences》2008,154(2):143-203
This paper is devoted to the computation of the radicals RN and RN* and the weakly solvable radical for a number of basic
classical linear groups over rings, including the unitary group over a ring with involution and matrix groups normalized by
elementary Chevalley groups.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 2, pp. 31–115, 2007. 相似文献
3.
James M. Turner 《Inventiones Mathematicae》2000,142(3):547-558
In this paper, we study the André-Quillen homology of simplicial commutative ℓ-algebras, ℓ a field, having certain vanishing
properties. When ℓ has non-zero characteristic, we obtain an algebraic version of a theorem of J.-P. Serre and Y. Umeda that
characterizes such simplicial algebras having bounded homotopy groups. We further discuss how this theorem fails in the rational
case and, as an application, indicate how the algebraic Serre theorem can be used to resolve a conjecture of D. Quillen for
algebras of finite type over Noetherian rings, having non-zero characteristic.
Oblatum 3-III-1999 & 3-V-2000?Published online: 11 October 2000 相似文献
4.
Every module over an Iwanaga–Gorenstein ring has a Gorenstein flat cover [13] (however, only a few nontrivial examples are
known). Integral group rings over polycyclic-by-finite groups are Iwanaga–Gorenstein [10] and so their modules have such covers.
In particular, modules over integral group rings of finite groups have these covers. In this article we initiate a study of
these covers over these group rings. To do so we study the so-called Gorenstein cotorsion modules, i.e. the modules that split
under Gorenstein flat modules. When the ring is ℤ, these are just the usual cotorsion modules. Harrison [16] gave a complete
characterization of torsion free cotorsion ℤ-modules. We show that with appropriate modifications Harrison's results carry
over to integral group rings ℤG when G is finite. So we classify the Gorenstein cotorsion modules which are also Gorenstein flat over these ℤG. Using these results we classify modules that can be the kernels of Gorenstein flat covers of integral group rings of finite
groups. In so doing we necessarily give examples of such covers. We use the tools we develop to associate an integer invariant
n with every finite group G and prime p. We show 1≤n≤|G : P| where P is a Sylow p-subgroup of G and gives some indication of the significance of this invariant. We also use the results of the paper to describe the co-Galois
groups associated to the Gorenstein flat cover of a ℤG-module.
Presented by A. Verschoren
Mathematics Subject Classifications (2000) 20C05, 16E65. 相似文献
5.
The Gleason–Pierce–Ward theorem gives constraints on the divisor and field size of a linear divisible code over a finite field
whose dimension is half of the code length. This result is a departure point for the study of self-dual codes. In recent years,
additive codes have been studied intensively because of their use in additive quantum codes. In this work, we generalize the
Gleason–Pierce–Ward theorem on linear codes over GF(q), q = p
m
, to additive codes over GF(q). The first step of our proof is an application of a generalized upper bound on the dimension of a divisible code determined
by its weight spectrum. The bound is proved by Ward for linear codes over GF(q), and is generalized by Liu to any code as long as the MacWilliams identities are satisfied. The trace map and an analogous
homomorphism on GF(q) are used to complete our proof.
相似文献
6.
Povilas Banys 《Lithuanian Mathematical Journal》2011,51(3):303-309
In [V. Paulauskas, On Beveridge–Nelson decomposition and limit theorems for linear random fields, J. Multivariate Anal., 101:621–639, 2010], limit theorems for linear random fields generated by independent identically distributed innovations
were proved. In this paper, we present the central limit theorem for linear random fields with martingale-differences innovations
satisfying the central limit theorem from [J. Dedecker, A central limit theorem for stationary random fields, Probab. Theory Relat. Fields, 110(3):397–426, 1998] and arranged in lexicographical order. 相似文献
7.
We present an elementary proof of the Karush–Kuhn–Tucker Theorem for the problem with nonlinear inequality constraints and
linear equality constraints. Most proofs in the literature rely on advanced optimization concepts such as linear programming
duality, the convex separation theorem, or a theorem of the alternative for systems of linear inequalities. By contrast, the
proof given here uses only basic facts from linear algebra and the definition of differentiability. 相似文献
8.
Igor Klep 《Algebras and Representation Theory》2007,10(5):429-439
We study some classes of ordered domains that are embeddable in division rings. We prove the ordered version of the Cohn–Lichtman
embedding theorem for valued domains. A question of Glass is answered in the negative. Furthermore, we prove that universal
enveloping algebras of Lie algebras over formally real fields can be embedded into ordered division rings.
The author acknowledges the financial support from the state budget by the Slovenian Research Agency (project no. Z1-9570-0101-06). 相似文献
9.
B. V. Tarasov 《Mathematical Notes》1977,22(3):742-748
A theorem of inertness for a class of semigroup rings is proved. An example showing that this class of rings is not totally
inert is constructed.
Translated from Matematicheskie Zametki, Vol. 22, No. 3, pp. 453–463, September, 1977.
The author thanks L. A. Bokut' for assistance with the article. 相似文献
10.
11.
S. V. Vostokov 《Journal of Mathematical Sciences》1990,52(3):3133-3141
One considers the structure of the group of the points of a formal group and its Lutz filtration as a Galois module in an
extension without higher ramification of a local field. Making use, on one hand, of Honda's theory on the classification of
formal groups over complete local rings and, on the other hand, of a generalization to formal groups of the Artin-Hasse function,
one constructs effectively an isomorphism between the group of points and some given additive free Galois module. In particular,
in the multiplicative case one gives a new effective proof of Krasner's theorem on the normal basis of the group of principal
units of a local field in extensions without higher ramification.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR,
Vol. 160, pp. 182–192, 1987. 相似文献
12.
By using the degree matrix, we provide an elementary and algorithmic approach to estimating the divisibility of exponential
sums over prime fields, which improves the Adolphson–Sperber theorem obtained by using the Newton polyhedron. Our result also
improves the Ax–Katz theorem on estimating the number of rational points on hypersurfaces over prime fields. 相似文献
13.
M. S. Burgin 《Mathematical Notes》1974,16(3):867-872
With the aid of mixed linear Ω-algebras we prove a theorem to the effect that the cancellation law is satisfied in a groupoid of subvarieties of a variety of Ω-algebras linear over a field and given by identities of zero order. We show that in some varieties of Ω-algebras linear over an infinite ring of principal ideals there are no nontrivial finitely attainable subvarieties. As examples of such varieties we cite the varieties of all Ω-rings, of all rings, of commutative or anticommutative rings (Ω-rings), of Lie rings, et al. In the case of anticommutative rings (Ω-rings) this property holds for Ω-algebras, linear over an arbitrary integral domain without stable ideals. 相似文献
14.
The Orlik–Solomon algebra of a matroid can be considered as a quotient ring over the exterior algebra E. At first, we study homological properties of E-modules as e.g., complexity, depth and regularity. In particular, we consider modules with linear injective resolutions.
We apply our results to Orlik–Solomon algebras of matroids and give formulas for the complexity, depth and regularity of such
rings in terms of invariants of the matroid. Moreover, we characterize those matroids whose Orlik–Solomon ideal has a linear
projective resolution and compute in these cases the Betti numbers of the ideal. 相似文献
15.
A theorem on the presentability of a multiple integral as a linear form in 1, ζ(3), ζ(5),..., ζ(2k − 1) over ℚ is proved. This theorem refines the results recently obtained by D. Vasiliev, V. Zudilin, and S. Zlobin.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 6, pp. 143–178, 2005. 相似文献
16.
Eimear Byrne Marcus Greferath Axel Kohnert Vitaly Skachek 《Designs, Codes and Cryptography》2010,57(2):169-179
We give further results on the question of code optimality for linear codes over finite Frobenius rings for the homogeneous
weight. This article improves on the existing Plotkin bound derived in an earlier paper (Greferath and O’Sullivan, Discr Math
289:11–24, 2004) and suggests a version of a Singleton bound. We also present some families of codes meeting these new bounds. 相似文献
17.
P. M. Akhmet’ev 《Journal of Mathematical Sciences》2009,159(6):753-760
In this paper, a geometric approach to stable homotopy groups of spheres based on the Pontryagin–Thom construction is proposed.
From this approach, a new proof of the Hopf-invariant-one theorem of J. F. Adams for all dimensions except 15, 31, 63, and
127 is obtained. It is proved that for n > 127, in the stable homotopy group of spheres Π
n
, there is no element with Hopf invariant one. The new proof is based on geometric topology methods. The Pontryagin–Thom theorem
(in the form proposed by R. Wells) about the representation of stable homotopy groups of the real, projective, infinite-dimensional
space (these groups are mapped onto 2-components of stable homotopy groups of spheres by the Kahn–Priddy theorem) by cobordism
classes of immersions of codimension 1 of closed manifolds (generally speaking, nonoriented) is considered. The Hopf invariant
is expressed as a characteristic class of the dihedral group for the self-intersection manifold of an immersed codimension-1
manifold that represents the given element in the stable homotopy group. In the new proof, the geometric control principle
(by M. Gromov) for immersions in the given regular homotopy classes based on the Smale–Hirsch immersion theorem is required.
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 8, pp. 3–15, 2007. 相似文献
18.
Jeroen Kuipers Dries Vermeulen Mark Voorneveld 《International Journal of Game Theory》2010,39(4):585-602
The Shapley–Ichiishi result states that a game is convex if and only if the convex hull of marginal vectors equals the core.
In this paper, we generalize this result by distinguishing equivalence classes of balanced games that share the same core
structure. We then associate a system of linear inequalities with each equivalence class, and we show that the system defines
the class. Application of this general theorem to the class of convex games yields an alternative proof of the Shapley–Ichiishi
result. Other applications range from computation of stable sets in non-cooperative game theory to determination of classes
of TU games on which the core correspondence is additive (even linear). For the case of convex games we prove that the theorem
provides the minimal defining system of linear inequalities. An example shows that this is not necessarily true for other
equivalence classes of balanced games. 相似文献
19.
Vasco Brattka 《Archive for Mathematical Logic》2008,46(7-8):547-564
The classical Hahn–Banach Theorem states that any linear bounded functional defined on a linear subspace of a normed space
admits a norm-preserving linear bounded extension to the whole space. The constructive and computational content of this theorem
has been studied by Bishop, Bridges, Metakides, Nerode, Shore, Kalantari Downey, Ishihara and others and it is known that
the theorem does not admit a general computable version. We prove a new computable version of this theorem without unrolling
the classical proof of the theorem itself. More precisely, we study computability properties of the uniform extension operator
which maps each functional and subspace to the set of corresponding extensions. It turns out that this operator is upper semi-computable
in a well-defined sense. By applying a computable version of the Banach–Alaoglu Theorem we can show that computing a Hahn–Banach
extension cannot be harder than finding a zero in a compact metric space. This allows us to conclude that the Hahn–Banach
extension operator is -computable while it is easy to see that it is not lower semi-computable in general. Moreover, we can derive computable versions
of the Hahn–Banach Theorem for those functionals and subspaces which admit unique extensions.
This work has been partially supported by the National Research Foundation (NRF) Grant FA2005033000027 on “Computable Analysis
and Quantum Computing”. An extended abstract version has been published in the conference proceedings [7]. 相似文献
20.
I. N. Balaba 《Journal of Mathematical Sciences》2008,152(4):451-455
We prove the analogue of Bolla’s theorem that isomorphisms of graded endomorphism rings of progenerators are induced by the
graded Morita equivalence
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 1, pp. 3–10, 2007. 相似文献