共查询到20条相似文献,搜索用时 31 毫秒
1.
2.
Elena Liliana Popescu 《Journal of Pure and Applied Algebra》2008,212(6):1427-1431
Let be the absolute Galois group of Q and let A=C(G,C) be the Banach algebra of all continuous functions defined on G with values in C. Let be the conjugation automorphism of C and let B be the R-Banach subalgebra of A consisting of continuous functions f such that for all σ∈G. Let ‖x‖=sup{|σ(x)|:σ∈G} be the spectral norm on and let be the spectral completion of . Using a canonical isometry between and B we study the structure of the group of R-algebras automorphisms of and the structure of its subgroup of all automorphisms of which when restricted to give rise to elements of G. We introduce a topology on and prove that this last one is homeomorphic and group isomorphic to G. 相似文献
3.
For a commutative ring R with zero-divisors Z(R), the zero-divisor graph of R is Γ(R)=Z(R)−{0}, with distinct vertices x and y adjacent if and only if xy=0. In this paper, we characterize when either or . We then use these results to investigate the diameter and girth for the zero-divisor graphs of polynomial rings, power series rings, and idealizations. 相似文献
4.
Reza Sazeedeh 《Journal of Pure and Applied Algebra》2008,212(1):275-280
Let R=?n∈N0Rn be a Noetherian homogeneous ring with local base ring (R0,m0) and irrelevant ideal R+, let M be a finitely generated graded R-module. In this paper we show that is Artinian and is Artinian for each i in the case where R+ is principal. Moreover, for the case where , we prove that, for each i∈N0, is Artinian if and only if is Artinian. We also prove that is Artinian, where and c is the cohomological dimension of M with respect to R+. Finally we present some examples which show that and need not be Artinian. 相似文献
5.
6.
Stefania Gabelli Evan Houston Thomas G. Lucas 《Journal of Pure and Applied Algebra》2004,194(3):281-298
Generalizing work of Gilmer and Heinzer, we define a t#-domain to be a domain R in which for any two distinct subsets and of the set of maximal t-ideals of R. We provide characterizations of these domains, and we show that polynomial rings over t#-domains are again t#-domains. Finally, we study overrings of t#-domains. 相似文献
7.
8.
C?t?lin Ciuperc? 《Journal of Pure and Applied Algebra》2003,178(1):25-48
Let A be a local ring with maximal ideal . For an arbitrary ideal I of A, we define the generalized Hilbert coefficients . When the ideal I is -primary, jk(I)=(0,…,0,(−1)kek(I)), where ek(I) is the classical kth Hilbert coefficient of I. Using these coefficients we give a numerical characterization of the homogeneous components of the S2-ification of S=A[It,t−1], extending previous results obtained by the author to not necessarily -primary ideals. 相似文献
9.
Najib Ouled Azaiez 《Journal of Number Theory》2008,128(7):1966-1988
We describe the additive structure of the graded ring of quasimodular forms over any discrete and cocompact group Γ⊂PSL(2,R). We show that this ring is never finitely generated. We calculate the exact number of new generators in each weight k. This number is constant for k sufficiently large and equals where I and are the ideals of modular forms and quasimodular forms, respectively, of positive weight. We show that is contained in some finitely generated ring of meromorphic quasimodular forms with i.e., the same order of growth as 相似文献
10.
Steve Seif 《Journal of Pure and Applied Algebra》2008,212(5):1162-1174
A classic result from the 1960s states that the asymptotic growth of the free spectrum of a finite group is sub-log-exponential if and only if is nilpotent. Thus a monoid is sub-log-exponential implies , the pseudovariety of semigroups with nilpotent subgroups. Unfortunately, little more is known about the boundary between the sub-log-exponential and log-exponential monoids.The pseudovariety consists of those finite semigroups satisfying (xωyω)ω(yωxω)ω(xωyω)ω≈(xωyω)ω. Here it is shown that a monoid is sub-log-exponential implies . A quick application: a regular sub-log-exponential monoid is orthodox. It is conjectured that a finite monoid is sub-log-exponential if and only if it is , the finite monoids in having nilpotent subgroups. The forward direction of the conjecture is proved; moreover, the conjecture is proved for when is completely (0)-simple. In particular, the six-element Brandt monoid (the Perkins semigroup) is sub-log-exponential. 相似文献
11.
Zhi-Hong Sun 《Journal of Number Theory》2005,113(1):10-52
Let be a prime, m∈Z and . In this paper we obtain a general criterion for m to be a quartic residue in terms of appropriate binary quadratic forms. Let d>1 be a squarefree integer such that , where is the Legendre symbol, and let εd be the fundamental unit of the quadratic field . Since 1942 many mathematicians tried to characterize those primes p so that εd is a quadratic or quartic residue . In this paper we will completely solve these open problems by determining the value of , where p is an odd prime, and . As an application we also obtain a general criterion for , where {un(a,b)} is the Lucas sequence defined by and . 相似文献
12.
13.
Let γ be the Gauss measure on and the Ornstein-Uhlenbeck operator. For every p in [1,∞)?{2}, set , and consider the sector . The main results of this paper are the following. If p is in (1,∞)?{2}, and , i.e., if M is an Lp(γ)uniform spectral multiplier of in our terminology, and M is continuous on , then M extends to a bounded holomorphic function on the sector . Furthermore, if p=1 a spectral multiplier M, continuous on , satisfies the condition if and only if M extends to a bounded holomorphic function on the right half-plane, and its boundary value M(i·) on the imaginary axis is the Euclidean Fourier transform of a finite Borel measure on the real line. We prove similar results for uniform spectral multipliers of second order elliptic differential operators in divergence form on belonging to a wide class, which contains . From these results we deduce that operators in this class do not admit an H∞ functional calculus in sectors smaller than . 相似文献
14.
15.
16.
17.
18.
We estimate the norm of the almost Mathieu operator , regarded as an element in the rotation C*-algebra . In the process, we prove for every λ∈R and the inequality
19.
20.
Joachim Toft 《Bulletin des Sciences Mathématiques》2003,127(2):101-132
We study , of all such that for every ?∈C∞0, where denotes the twisted convolution. We prove that certain boundedness for are completely determined of the behaviour for a at origin, for example that , and that if a(0)<∞, then a∈L2∩L∞. We use the results in order to determine wether positive pseudo-differential operators belong to certain Schatten-casses or not. 相似文献