In this paper we study relative and Tate cohomology of modules of finite Gorenstein injective dimension. Using these cohomology theories, we present variations of Grothendieck local cohomology modules, namely Gorenstein and Tate local cohomology modules. By applying a sort of Avramov-Martsinkovsky exact sequence, we show that these two variations of local cohomology are tightly connected to the generalized local cohomology modules introduced by J. Herzog. We discuss some properties of these modules and give some results concerning their vanishing and non-vanishing.
We prove that any infinitely generated tilting module is of finite type, namely that its associated tilting class is the Ext-orthogonal of a set of modules possessing a projective resolution consisting of finitely generated projective modules.
The positive extended KdV equation with self-consistent sources (eKdV+ ESCSs) is firstly presented and its related linear auxiliary equation is derived. The generalized binary Darboux transformation (DT) is applied to construct some new solutions of the eKdV+ ESCSs such as N-soliton solution, N-double pole solution and nonsingular N-positon solution. The properties of these solutions are analyzed. Moreover, the interaction of two solitons is discussed in detail. 相似文献
Let be a Noetherian homogeneous ring with one-dimensional local base ring . Let be an -primary ideal, let be a finitely generated graded -module and let . Let denote the -th local cohomology module of with respect to the irrelevant ideal 0} R_n$"> of . We show that the first Hilbert-Samuel coefficient of the -th graded component of with respect to is antipolynomial of degree in . In addition, we prove that the postulation numbers of the components with respect to have a common upper bound.
In this paper, the theory of local homology for Artinian modules is developed, which in some aspect is similar to the theory of local cohomology. There are given some criteria for local homology modules to be good and dual of the ideal transform functor is studied.AMS Subject Classification (1991): 13E10 13D45 相似文献
We show that over an elliptic algebra, critical modules of Gelfand-Kirillov dimension 2 exist in all multiplicities (assuming the ground field is uncountable, algebraically closed). Geometrically, this shows that in a quantum plane there exist ``irreducible curve" modules of all possible degrees.
We prove that the Kauffman bracket skein algebra of the cylinder over a torus is a canonical subalgebra of the noncommutative torus. The proof is based on Chebyshev polynomials. As an application, we describe the structure of the Kauffman bracket skein module of a solid torus as a module over the algebra of the cylinder over a torus, and recover a result of Hoste and Przytycki about the skein module of a lens space. We establish simple formulas for Jones-Wenzl idempotents in the skein algebra of a cylinder over a torus, and give a straightforward computation of the -th colored Kauffman bracket of a torus knot, evaluated in the plane or in an annulus.
Let be a subring of the rationals. We want to investigate self splitting -modules (that is . Following Schultz, we call such modules splitters. Free modules and torsion-free cotorsion modules are classical examples of splitters. Are there others? Answering an open problem posed by Schultz, we will show that there are more splitters, in fact we are able to prescribe their endomorphism -algebras with a free -module structure. As a by-product we are able to solve a problem of Salce, showing that all rational cotorsion theories have enough injectives and enough projectives. This is also basic for answering the flat-cover-conjecture.
We show that, if is a representation-finite iterated tilted algebra of euclidean type , then there exist a sequence of algebras , and a sequence of modules , where , such that each is an APR-tilting -module, or an APR-cotilting -module, and is tilted representation-finite.
