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1.
Let R and S be associative rings and _SV_R a semidualizing(S-R)-bimodule. An R-module N is said to be V-Gorenstein injective if there exists a Hom_R(I_V(R),-) and Hom_R(-, I_V(R)) exact exact complex ···→ I_1 d_0→I_0→I~0 d_0→I~1→··· of V-injective modules I_i and I~i, i ∈ N_0, such that N≌Im(I_0→I~0). We will call N to be strongly V-Gorenstein injective in case that all modules and homomorphisms in the above exact complex are equal, respectively. It is proved that the class of V-Gorenstein injective modules are closed under extension, direct summand and is a subset of the Auslander class A_V(R) which leads to the fact that V-Gorenstein injective modules admit exact right I_V(R)-resolution. By using these facts, and thinking of the fact that the class of strongly V-Gorenstein injective modules is not closed under direct summand, it is proved that an R-module N is strongly VGorenstein injective if and only if N⊕E is strongly V-Gorenstein injective for some V-injective module E. Finally, it is proved that an R-module N of finite V-Gorenstein injective injective dimension admits V-Gorenstein injective preenvelope which leads to the fact that, for a natural integer n, Gorenstein V-injective injective dimension of N is bounded to n if and only if Ext_(IV(R))~(≥n+1)(I, N) = 0 for all modules I with finite I_V(R)-injective dimension.  相似文献   

2.
Let A be a monomial quasi-hereditary algebra with a pure strong exact Borel subalgebra B.It is proved that the category of induced good modules over B is contained in the category of good modules over A;that the characteristic module of A is an induced module of that of B via the exact functor-(?)_B A if and only if the induced A-module of an injective B-module remains injective as a B-module.Moreover,it is shown that an exact Borel subalgebra of a basic quasi-hereditary serial algebra is right serial and that the characteristic module of a basic quasi-hereditary serial algebra is exactly the induced module of that of its exact Borel subalgebra.  相似文献   

3.
郭辉 《数学进展》2004,33(3):373-374
Let A, B be two sets and f:A→B a map. The iterates f~n: A_n→B,n=1,2,…aredefined inductively by A_1=A, f~1=f and A_1=f~(-1)(A_(n-1)∩B), f~n=f~(n-1)(f) for n≥2.Note that A_2=f~(-1)(A_1∩B)A=A_1 and thus A_n A_(n-1) A for n≥2. A point x∈A is called a periodic point of period n of f if x∈A_n and f~n(x)=x, butf_j(x)≠x for any j less than n. A periodic point of period 1 is called a fixpoint. Then a periodic  相似文献   

4.
For a tuple A=(A_1,A_2,…,A_n) of elements in a unital algebra B over C,its projective spectrum P(A) or p(A) is the collection of z∈C~n,or respectively z∈P~(n-1),such that A(z)=z_1A_1+z_2A_2+…+z_nA_n is not invertible in Β.The first half of this paper proves that if B is Banach then the resolvent set P~c(A) consists of domains of holomorphy.The second half computes the projective spectrum for the generating vectors of a Clifford algebra.The Chern character of an associated kernel bundle is shown to be nontrivial.  相似文献   

5.
This paper is devoted to proving the following fact :Let G be a Gabriel topology, E an injective module cogenerating torsion theory (T, F) associated to G. NG= (0≠M∈F|M/L∈T for every nonzero submodu-le L?M} . then, M∈NG if and only if1) M is uniform,2) every nonzero homomorphism form M into M is injective,3) M is a quasi-essential submodule of E.At the same time, we proved that if a module M∈NG then M, MG∈NG.Fi-nally, we considered critically compressible modules, under the assumption that Gabriel topology G is perfect.  相似文献   

6.
In this paper, we investigate Ding projective dimensions and Ding injective dimensions of modules and ringsLet R be a ring with r DP D(R) = n ∞, and let W1 = {M|fd(M) ∞}We prove that(DP, W1) is a complete hereditary cotorsion pair such that a module M belongs to DP ∩ W1 if and only if M is projective, moreover,W1 = {M|pd(M) ∞} = {M|fd(M) ≤ n} = {M|pd(M) ≤ n}Then we introduce and investigate Ding derived functor Dexti(-,-), and use it to characterize global Ding dimensionWe show that if R is a Ding-Chen ring, or if R is a ring with r DP D(R) ∞ and r DI D(R) ∞,then r DP D(R) ≤ n if and only if r DI D(R) ≤ n if and only if Dextn+i(M, N) = 0 for all modules M and N and all integer i ≥ 1.  相似文献   

7.
This paper studios the existence of closed geodesics in the homotopy class of a given closed curve. Let M be a complete Riemannian manifold without boundary, f∈C~1(S~1, M). Look at S~1 as [0, 2π]/{0, 2π}. The following results are proved:A. The initial value problem of heat equation _if_t=τ(f_i), f_0=f always admits a global solution.B. (Existence of closed geodesics). If there exists a compact set KM such that f(S~1)∩K≠φ andE(f)≤(1/π)l(K)~2,then there exists a closed geodesic homotopic to f. If then the closed geodesic is minimal.C. Some estimates about injective radius are obtained.Some example is found showing that the inequalities in B are sharp.  相似文献   

8.
Let (K, M,H) be an upper triangular bimodule problem. Briistle and Hille showed that the opposite algebra A of the endomorphism algebra of a projective generator P of the matrices category of (K., M, H) is quasi-hereditary, and there is an equivalence between the category of△-good modules of A and Mat(K, M). In this note, based on the tame theorem for bimodule problems, we show that if the algebra A associated with an upper triangular bimodule problem is of△-tame representation type, then the category F(△) has the homogeneous property, i.e. almost all modules in F(△) are isomorphic to their Auslander-Reiten translations. Moreover, if (K, M,H)is an upper triangular bipartite bimodule problem, then A is of△-tame representation type if and only if F(△) is homogeneous.  相似文献   

9.
Let A be a j x d (0,1) matrix. It is known that if j = 2k - 1 is odd, then det(AAT) ≤ (j+1)((j+1)d/4j)j; if j is even, then det(AAT) ≤ (j+1)((j+2)d/4(j+1))j. A is called a regular D-optimal matrix if it satisfies the equality of the above bounds. In this note, it is proved that if j = 2k - 1 is odd, then A is a regular D-optimal matrix if and only if A is the adjacent matrix of a (2k - 1, k, (j + l)d/4j)-BIBD; if j = 2k is even, then A is a regular D-optimal matrix if and only if A can be obtained from the adjacent matrix B of a (2k + 1,k + 1,(j + 2)d/4(j +1))-BIBD by deleting any one row from B. Three 21 x 42 regular D-optimal matrices, which were unknown in [11], are also provided.  相似文献   

10.
For a transitive Lie algebroid A on a connected manifold M and its representation on a vector bundle F, we define a morphism of cohomology groups rk: Hk(A,F) → Hk(Lx,Fx), called the localization map, where Lx is the adjoint algebra at x ∈ M. The main result in this paper is that if M is simply connected, or H (LX,FX) is trivial, then T is injective. This means that the Lie algebroid 1-cohomology is totally determined by the 1-cohomology of its adjoint Lie algebra in the above two cases.  相似文献   

11.
12.
We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.  相似文献   

13.
Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.  相似文献   

14.
张丽娜  吴建华 《数学进展》2008,37(1):115-117
One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the'living world. In his seminal paper "The Chemical Basis of Morphogenesis", Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates(1990) on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing's prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows  相似文献   

15.
It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.  相似文献   

16.
In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).  相似文献   

17.
18.
正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with  相似文献   

19.
正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.  相似文献   

20.
A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].  相似文献   

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