共查询到20条相似文献,搜索用时 31 毫秒
1.
Let R be a ring and P be an (infinite dimensional) partial tilting module. We show that the perpendicular category of P is equivalent to the full module category where and ?R is the Bongartz complement of P modulo its P-trace. Moreover, there is a ring epimorphism φ:R→S. We characterize the case when φ is a perfect localization. By [Riccardo Colpi, Alberto Tonolo, Jan Trlifaj, Partial cotilting modules and the lattices induced by them, Comm. Algebra 25 (10) (1997) 3225-3237], there exist mutually inverse isomorphisms μ′ and ν′ between the interval in the lattice of torsion classes in , and the lattice of all torsion classes in . We provide necessary and sufficient conditions for μ′ and ν′ to preserve tilting torsion classes. As a consequence, we show that these conditions are always satisfied when R is a Dedekind domain, and if P is finitely presented and R is an artin algebra, then the conditions reduce to the trivial ones, namely that each value of μ′ and ν′ contains all injectives. 相似文献
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P.N. Ánh 《Linear algebra and its applications》2011,434(4):1018-1026
We call a ring strongly indecomposable if it cannot be represented as a non-trivial (i.e. M≠0) generalized triangular matrix ring , for some rings R and S and some R-S-bimodule RMS. Examples of such rings include rings with only the trivial idempotents 0 and 1, as well as endomorphism rings of vector spaces, or more generally, semiprime indecomposable rings. We show that if R and S are strongly indecomposable rings, then the triangulation of the non-trivial generalized triangular matrix ring is unique up to isomorphism; to be more precise, if is an isomorphism, then there are isomorphisms ρ:R→R′ and ψ:S→S′ such that χ:=φ∣M:M→M′ is an R-S-bimodule isomorphism relative to ρ and ψ. In particular, this result describes the automorphism groups of such upper triangular matrix rings 相似文献
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Let φ:(R,m)→S be a flat ring homomorphism such that mS≠S. Assume that M is a finitely generated S-module with dimR(M)=d. If the set of support of M has a special property, then it is shown that if and only if for each prime ideal satisfying , we have . This gives a generalization of the Lichtenbaum-Hartshorne vanishing theorem for modules which are finite over a ring homomorphism. Furthermore, we provide two extensions of Grothendieck’s non-vanishing theorem. Applications to connectedness properties of the support are given. 相似文献
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Given a homomorphism of commutative noetherian rings ?:R→S, Daniel Quillen conjectured in 1970 that if the André-Quillen homology functors Dn(S∣R;−) vanish for all n?0, then they vanish for all n?3. We prove the conjecture under the additional hypothesis that there exists a homomorphism of rings ψ:S→R such that ?°ψ=idS. More precisely, in this case we show that ψ is a complete intersection at for every prime ideal of S. Using these results, we describe all algebra retracts S→R→S for which the algebra Tor•R(S,S) is finitely generated over Tor0R(S,S)=S. 相似文献
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Douglas S. Stones 《Journal of Combinatorial Theory, Series A》2010,117(2):204-215
A k×n Latin rectangle on the symbols {1,2,…,n} is called reduced if the first row is (1,2,…,n) and the first column is T(1,2,…,k). Let Rk,n be the number of reduced k×n Latin rectangles and m=⌊n/2⌋. We prove several results giving divisors of Rk,n. For example, (k−1)! divides Rk,n when k?m and m! divides Rk,n when m<k?n. We establish a recurrence which determines the congruence class of for a range of different t. We use this to show that Rk,n≡((−1)k−1(k−1)!)n−1. In particular, this means that if n is prime, then Rk,n≡1 for 1?k?n and if n is composite then if and only if k is larger than the greatest prime divisor of n. 相似文献
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Given a homomorphism of commutative noetherian rings R→S and an S-module N, it is proved that the Gorenstein flat dimension of N over R, when finite, may be computed locally over S. When, in addition, the homomorphism is local and N is finitely generated over S, the Gorenstein flat dimension equals , where E is the injective hull of the residue field of R. This result is analogous to a theorem of André on flat dimension. 相似文献
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Georges Gras 《Journal of Number Theory》2009,129(11):2843-2852
Let K be a number field, p a prime, and let be the T-ramified, S-split p-class field tower of K, i.e., the maximal pro-p-extension of K unramified outside T and totally split on S, where T and S are disjoint finite sets of places of K. Using a theorem of Tate on nilpotent quotient groups, we give (Theorem 2 in Section 3) an elementary characterisation of the finite extensions L/K, with a normal closure of degree prime to p, such that the analogous p-class field tower of L is equal to the compositum . This N.S.C. only depends on classes and units of L. Some applications and examples are given. 相似文献
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S. Albeverio 《Journal of Functional Analysis》2005,228(1):144-188
Let S be the orthogonal sum of infinitely many pairwise unitarily equivalent symmetric operators with non-zero deficiency indices. Let J be an open subset of R. If there exists a self-adjoint extension S0 of S such that J is contained in the resolvent set of S0 and the associated Weyl function of the pair {S,S0} is monotone with respect to J, then for any self-adjoint operator R there exists a self-adjoint extension such that the spectral parts and RJ are unitarily equivalent. It is shown that for any extension of S the absolutely continuous spectrum of S0 is contained in that one of . Moreover, for a wide class of extensions the absolutely continuous parts of and S are even unitarily equivalent. 相似文献
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S. Konyagin 《Journal of Number Theory》2007,124(1):193-199
We show that there exist arbitrarily large sets S of s prime numbers such that the equation a+b=c has more than solutions in coprime integers a, b, c all of whose prime factors lie in the set S. We also show that there exist sets S for which the equation a+1=c has more than solutions with all prime factors of a and c lying in S. 相似文献
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Ping-Bao Liao 《Linear algebra and its applications》2009,430(4):1236-197
Let A be a prime algebra of characteristic not 2 with extended centroid C, let R be a noncentral Lie ideal of A and let B be the subalgebra of A generated by R. If f,d:R→A are linear maps satisfying that
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Paolo Zanardo 《Journal of Pure and Applied Algebra》2008,212(10):2259-2270
Let R be a local one-dimensional domain. We investigate when the class semigroup S(R) of R is a Clifford semigroup. We make use of the Archimedean valuation domains which dominate R, as a main tool to study its class semigroup. We prove that if S(R) is Clifford, then every element of the integral closure of R is quadratic. As a consequence, such an R may be dominated by at most two distinct Archimedean valuation domains, and coincides with their intersection. When S(R) is Clifford, we find conditions for S(R) to be a Boolean semigroup. We derive that R is almost perfect with Boolean class semigroup if, and only if R is stable. We also find results on S(R), through examination of [V/P:R/M] and v(M), where V dominates R, and P, M are the respective maximal ideals. 相似文献
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Francis Gardeyn 《Journal of Number Theory》2003,100(2):332-362
Let R be a complete discrete valuation -algebra whose residue field is algebraic over , and let K denote its fraction field. In this paper, we study the structure of τ-sheaves M without good reduction on the curve , seen as a rigid analytic space. One motivation is the Tate uniformization theorem for t-motives of Drinfeld modules, which we want to extend to general τ-sheaves. On the other hand, we are interested in the action of inertia on a generic Tate module T?(M) of M.For a given τ-sheaf M on , we prove the existence of a maximal model for M on , an R-model of , and, over a finite separable extension R′ of R, of nondegenerate models for M.We prove the following ‘semistability’ theorem: there exists a finite extension K′ of K, a nonempty open subscheme C′⊂C, and a filtration
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Piotr Niemiec 《Topology and its Applications》2008,155(12):1323-1328
The aim of the paper is to generalize the notion of the Haar integral. For a compact semigroup S acting continuously on a Hausdorff compact space Ω, the algebra A(S)⊂C(Ω,R) of S-invariant functions and the linear space M(S) of S-invariant (real-valued) finite signed measures are considered. It is shown that if S has a left and right invariant measure, then the dual space of A(S) is isometrically lattice-isomorphic to M(S) and that there exists a unique linear operator (called the Haar integral) such that for each f∈A(S) and for any f∈C(Ω,R) and s∈S, , where . 相似文献
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Refael Hassin 《Operations Research Letters》2005,33(3):242-248
The input to the MAXIMUM SAVING PARTITION PROBLEM consists of a set V={1,…,n}, weights wi, a function f, and a family S of feasible subsets of V. The output is a partition (S1,…,Sl) such that Si∈S, and is maximized. We present a general -approximation algorithm, and improved algorithms for special cases of the function f. 相似文献
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Let ∥ · ∥ be the Frobenius norm of matrices. We consider (I) the set SE of symmetric and generalized centro-symmetric real n × n matrices Rn with some given eigenpairs (λj, qj) (j = 1, 2, … , m) and (II) the element in SE which minimizes for a given real matrix R∗. Necessary and sufficient conditions for SE to be nonempty are presented. A general form of elements in SE is given and an explicit expression of the minimizer is derived. Finally, a numerical example is reported. 相似文献
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Charles C.C. Li 《Journal of Number Theory》2004,104(1):177-192
Let (X,μ) be a measurable topological space. Let S1,S2,… be a family of finite subsets of X. Suppose each x∈Si has a weight wix∈R+ assigned to it. We say {Si} is {wi}-distributed with respect to the measure μ if for any continuous function f on X, we have .Let S(N,k) be the space of modular cusp forms over Γ0(N) of weight k and let be a basis which consists of Hecke eigenforms. Let ar(h) be the rth Fourier coefficient of h. Let xph be the eigenvalue of h relative to the normalized Hecke operator T′p. Let ||·|| be the Petersson norm on S(N,k). In this paper we will show that for any even integer k?3, is -distributed with respect to a polynomial times the Sato-Tate measure when N→∞. 相似文献
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Susana Coré 《Journal of Mathematical Analysis and Applications》2010,370(2):472-485
Let G be a homogeneous group with homogeneous dimension Q, and let So denote the space of Schwartz functions on G with all moments vanishing. Let be the usual Euclidean Fourier transform. For j∈R, we let be the space of J, smooth away from 0, satisfying |α∂J(ξ)|?Cβ|ξ|j−|β|, where both |ξ| and |β| are taken in the homogeneous sense. We characterize , and show that as elements of . If j1,j2,j1+j2>−Q, one can replace So, by S, S′ in this result. A key ingredient of our proof is a lemma from the fundamental wavelet paper from 1985 by Frazier and Jawerth [4]. We believe that, in turn, our result will be useful in the theory of wavelets on homogeneous groups. 相似文献