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1.
Structure of Degenerate Block Algebras   总被引：12，自引：0，他引：12
Given a non-trivial torsion-free abelian group (A,+,Q), a field F of characteristic 0, and a non-degenerate bi-additive skew-symmetric map : A A F, we define a Lie algebra = (A, ) over F with basis {ex | x A/{0}} and Lie product [ex,ey] = (x,y)ex+y. We show that is endowed uniquely with a non-degenerate symmetric invariant bilinear form and the derivation algebra Der of is a complete Lie algebra. We describe the double extension D( , T) of by T, where T is spanned by the locally finite derivations of , and determine the second cohomology group H2(D( , T),F) using anti-derivations related to the form on D( , T). Finally, we compute the second Leibniz cohomology groups HL2( , F) and HL2(D( , T), F).2000 Mathematics Subject Classification: 17B05, 17B30This work was supported by the NNSF of China (19971044), the Doctoral Programme Foundation of Institution of Higher Education (97005511), and the Foundation of Jiangsu Educational Committee.  相似文献
2.
Hochschild cohomology of truncated basic cycle   总被引：9，自引：0，他引：9
Dimensions of the Hochschild cohomology groups of a truncated algebra of a basic cycle are explicitly given. Project supported by the State Education Commission of China, the Chinese Academy of Sciences and the National Natural Science Foundation of China.  相似文献
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Deformation Theory and The Computation of Zeta Functions   总被引：3，自引：0，他引：3
We present a new approach to the problem of computing the zetafunction of a hypersurface over a finite field. For a hypersurfacedefined by a polynomial of degree d in n variables over thefield of q elements, one desires an algorithm whose runningtime is a polynomial function of dn log(q). (Here we assumed 2, for otherwise the problem is easy.) The case n = 1 isrelated to univariate polynomial factorisation and is comparativelystraightforward. When n = 2 one is counting points on curves,and the method of Schoof and Pila yields a complexity of , where the function Cd depends exponentiallyon d. For arbitrary n, the theorem of the author and Wan givesa complexity which is a polynomial function of (pdn log(q))n,where p is the characteristic of the field. A complexity estimateof this form can also be achieved for smooth hypersurfaces usingthe method of Kedlaya, although this has only been worked outin full for curves. The new approach we present should yielda complexity which is a small polynomial function of pdn log(q).In this paper, we work this out in full for Artin–Schreierhypersurfaces defined by equations of the form ZpZ= f, where the polynomial f has a diagonal leading form. Themethod utilises a relative p-adic cohomology theory for familiesof hypersurfaces, due in essence to Dwork. As a corollary ofour main theorem, we obtain the following curious result. Letf be a multivariate polynomial with integer coefficients whoseleading form is diagonal. There exists an explicit deterministicalgorithm which takes as input a prime p, outputs the numberof solutions to the congruence equation f = 0 op, and runs in bit operations, for any >0. This improves upon the elementary estimate of bit operations, where n is the number of variables,which can be achieved using Berlekamp's root counting algorithm.2000 Mathematics Subject Classification 11Y99, 11M38, 11T99.  相似文献
7.
Line bundles on non-primary Hopf manifolds   总被引：3，自引：0，他引：3
Let X be a Hopf manifolds with Abelian fundamental group, L any flat line bundle on X, we give a formula for computing explicitly the cohomology Hq(X,Ωp(L) using the method of group action and the generalized Douady sequence.  相似文献
8.
The f-depth of an ideal on a module   总被引：2，自引：0，他引：2
Let be an ideal of a Noetherian local ring and a finitely generated -module. The f-depth of on is the least integer such that the local cohomology module is not Artinian. This paper presents some part of the theory of f-depth including characterizations of f-depth and a relation between f-depth and f-modules.
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Suppose a group G acts on a Gromov-hyperbolic space X properlydiscontinuously. If the limit set L(G) of the action has atleast three points, then the second bounded cohomology groupof is infinite dimensional. For example, if M is a complete, pinched negatively curved Riemannianmanifold with finite volume, then is infinite dimensional. As an application, we show that ifG is a knot group with GZ, then is infinite dimensional. 1991 Mathematics Subject Classification:primary 20F32; secondary 53C20, 57M25.  相似文献
10.
ON THE COHOMOLOGY OF GENERALIZED RESTRICTED LIE ALGEBRAS   总被引：2，自引：0，他引：2
0.IntroductionThispaperisaimedatdevelopingthecohomologytheoryofmodularLiealgebrasandthendeterminingthefirstcohomologygroupsofCartantypeLiealgebras.AsgeneralizationoftheconceptofrestrictedLiealgebras,ageneralizedrestrictedLiealgebra(GRLiealgebra)wasintroducedin,whichisassociatedwithabasisandamappingofthebasisintotheLiealgebrasatisfyingthegeneralized-restrictednessconditions.Generalizedrestrictedrepresentations(GRrepresentations)werethenintroduced,whichcanbereducedtotherepresentationsofa…  相似文献