共查询到20条相似文献,搜索用时 218 毫秒
1.
Mohammad Ashraf 《Results in Mathematics》1993,24(3-4):201-210
In the present paper we first establish decomposition theorems for near rings satisfying either of the properties xy = xmypxn or xy = ymxpyn, where m≥1, n≥1, p≥1 are positive integers depending on the pair of near ring elements x,y; and further, we investigate commutativity of such near rings. Moreover, it is also shown that under some additional hypotheses, such nearrings turn out to be commutative rings. 相似文献
2.
We first establish the commutativity for the semiprime ring satisfying [x
n
, y]x
r = ±y
s[x, y
m]y
t for all x, y in R, where m, n, r, s, and t are fixed non-negative integers, and further, we investigate the commutativity of rings with unity under some additional hypotheses. Moreover, it is also shown that the above result is true for s-unital rings. Also, we provide some counterexamples which show that the hypotheses of our theorems are not altogether superfluous. The results of this paper generalize some of the well-known commutativity theorems for rings which are right s-unital. 相似文献
3.
We study commutativity of rings R with the property that for each nonperiodic element x of R there exists a positive integer K = K(x) such that xk is central for all k≥K. 相似文献
4.
Firstly,the commutativity of rings is investigated in this paper.Let R be a ring with identity.Then we obtain the following commutativity conditions: (1) if for each x ∈ R\N(R) and each y ∈ R,(xy)k =xkyk for k =m,m + 1,n,n + 1,where m and n are relatively prime positive integers,then R is commutative;(2) if for each x ∈ R\J(R) and each y ∈ R,(xy)k =ykxk for k =m,m+ 1,m+2,where m is a positive integer,then R is commutative.Secondly,generalized 2-CN rings,a kind of ring being commutative to some extent,are investigated.Some relations between generalized 2-CN rings and other kinds of rings,such as reduced rings,regular rings,2-good rings,and weakly Abel rings,are presented. 相似文献
5.
《Quaestiones Mathematicae》2013,36(2):173-182
Abstract A ring R is called pseudo-commutative if for each x,y ε R there exists an integer n = n(x, y) for which xy = nyx. We first show that a generalization of a commutativity condition of Chacron and Thierrin implies pseudo-commutativity in rings; we then study pseudo-commutativity and commutativity in rings with constraints of the form xy = σkiyixi, where the ki are integers. 相似文献
6.
Adil Yaqub 《Results in Mathematics》2006,49(3-4):377-386
A well-known theorm of Jacobson asserts that a ring R with the property that for every x in R there exists an integer n(x) > 1 such that xn(x) = x is necessarily commutative. With this as motivation, we define an N0-ring to be a ring which satisfies a weaker hypothesis than the “xn(x) = x” condition in Jacobson’s Theorem. We consider commutativity of N0-rings, usually with the additional hypothesis that the ground ring is also weakly periodic-like. 相似文献
7.
Markus Brodmann 《manuscripta mathematica》1992,76(1):181-192
Let M be a generalized Cohen-Macaulay module over a noetherian local ring (R,m). Fix a standard system x1, …, xd∈m with respect to M and let
. We construct a coherent Cohen-Macaulay sheafK over the projective space ℙ
R/I
d-1
whose cohomological Hilbert functions depend only on the lengths of the local cohomology modules H
m
i
(M), (i=0, …, d−1). 相似文献
8.
Commutativity of Rings with Constraints Involving a Subset 总被引:1,自引:0,他引:1
Moharram A. Khan 《Czechoslovak Mathematical Journal》2003,53(3):545-559
Suppose that R is an associative ring with identity 1, J(R) the Jacobson radical of R, and N(R) the set of nilpotent elements of R. Let m 1 be a fixed positive integer and R an m-torsion-free ring with identity 1. The main result of the present paper asserts that R is commutative if R satisfies both the conditions(i) [x
m, y
m] = 0 for all
and(ii) [(xy)
m
+ y
m
x
m, x] = 0 = [(yx)
m
+ x
m
y
m, x], for all
This result is also valid if (i) and (ii) are replaced by (i) [x
m, y
m] = 0 for all
and (ii) [(xy)
m
+ y
m
x
m, x] = 0 = [(yx)
m
+ x
m
y
m, x] for all
Other similar commutativity theorems are also discussed. 相似文献
9.
Jürgen Herzog 《manuscripta mathematica》1974,12(3):217-248
Let R be a commutative noetherian ring with unit. To a sequencex:=x1,...,xn of elements of R and an m-by-n matrix α:=(αij) with entries in R we assign a complex D*(x;α), in case that m=n or m=n?1. These complexes will provide us in certain cases with explicit minimal free resolutions of ideals, which are generated by the elements ai:=∑αijxj and the maximal minors of α. 相似文献
10.
A. Dubickas 《Journal of Mathematical Sciences》2006,137(2):4654-4657
Let g and m be two positive integers, and let F be a polynomial with integer coefficients. We show that the recurrent sequence
x0 = g, xn = x
n−1
n
+ F(n), n = 1, 2, 3,…, is periodic modulo m. Then a special case, with F(z) = 1 and with m = p > 2 being a prime number,
is considered. We show, for instance, that the sequence x0 = 2, xn = x
n−1
n
+ 1, n = 1, 2, 3, …, has infinitely many elements divisible by every prime number p which is less than or equal to 211 except
for three prime numbers p = 23, 47, 167 that do not divide xn. These recurrent sequences are related to the construction of transcendental numbers ζ for which the sequences [ζn!], n = 1, 2, 3, …, have some nice divisibility properties. Bibliography: 18 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 322, 2005, pp. 76–82. 相似文献
11.
Giovanni Di Lena Davide Franco Mario Martelli Basilio Messano 《Mediterranean Journal of Mathematics》2011,8(4):473-489
The main purpose of this paper is to investigate dynamical systems
F : \mathbbR2 ? \mathbbR2{F : \mathbb{R}^2 \rightarrow \mathbb{R}^2} of the form F(x, y) = (f(x, y), x). We assume that
f : \mathbbR2 ? \mathbbR{f : \mathbb{R}^2 \rightarrow \mathbb{R}} is continuous and satisfies a condition that holds when f is non decreasing with respect to the second variable. We show that for every initial condition x0 = (x
0, y
0), such that the orbit
O(x0) = {x0, x1 = F(x0), x2 = F(x1), . . . }, O({\rm{x}}_0) = \{{\rm{x}}_0, {\rm{x}}_1 = F({\rm{x}}_0), {\rm{x}}_2 = F({\rm{x}}_1), . . . \}, 相似文献
12.
Let (X m+1, g) be a globally hyperbolic spacetime with Cauchy surface diffeomorphic to an open subset of ${\mathbb{R}^{m}}
13.
Let R be a unital *-ring with the unit I.Assume that R contains a symmetric idempotent P which satisfies ARP = 0 implies A = 0 and AR(I-P) = 0 implies A = 0.In this paper,it is shown that a surjective map Φ:R→R is strong skew commutativity preserving(that is,satisfiesΦ(A)Φ(B)-Φ(B)Φ(A)~w= AB-BA~w for all A,B∈R) if and only if there exist a map f:R→Z_s(R)and an element Z∈Z_s(R) with Z~2=I such that Φ(A)=ZA +f(A) for all A∈R,where Z_s(R) is the symmetric center of R.As applications,the strong skew commutativity preserving maps on unital prime *-rings and von Neumann algebras with no central summands of type I_1 are characterized. 相似文献
14.
In this article we consider the self-adjoint operator governing the propagation of elastic waves in a perturbed isotropic half space with a free boundary condition. We prove the limiting absorption principle in appropriate Hilbert spaces for this operator. We also prove decreasing properties for the eigenfunctions associated with strictly positive eigenvalues of this operator. The proofs are based on the limiting absorption principle for the self-adjoint operator governing the propagation of elastic waves in a homogeneous isotropic half space with a free boundary and on the so called division theorem for it. Both perturbations of R +2 ={(x1, x2) ? R 2; x2 > 0} and R +2 = {(x1, x2, x3) ? R 3; x3 > 0} are considered. 相似文献
15.
Hongfei Zhang 《Applicable analysis》2013,92(1-4):107-137
The singular diffusion equation ut=(u?1ux)x:arises in many areas of application, e.g. in the central limit approximation to Carleman's model of Boltzman equation, or, in the expansion of a thermalized electron cloud in plasma physics. This paper concerns the existence and uniqueness of solution of a mixed boundary value problem of equation ut=(um=1ux)x for ?1 < m ≤0. 相似文献
16.
J.K. Verma 《代数通讯》2013,41(12):2999-3024
Let (R,m) be a local ring. Let SM denote the Rees algebra S=R[mrt] localized at its unique maximal homogeneous ideal M=(m,mrt). Let TN denote the extended Rees algebra T= R[mrt, t-1] localized at its unique maximal homogeneous idea N= (t?1,m,mr). Multiplicity formulas are developedfor SM and TN. These are used to find necessaIy and sufficient conditions on a Cohen-Macaulay local ring (R,m) and r so that SM and TN are Cohen-Macaulay with minimal multiplicity 相似文献
17.
Let R be a ring and d : R → R a derivation of R. In the present paper we investigate commutativity of R satisfying any one of the properties (i)d([x,y]) = [x,y], (ii)d(x o y) = xoy, (iii)d(x) o d(y) = 0, or (iv)d(x) o d(y) = x o y, for all x, y in some apropriate subset of R. 相似文献
18.
Cheng-Kai Liu 《Algebras and Representation Theory》2013,16(6):1561-1576
We investigate the commutativity in a (semi-)prime ring R which admits skew derivations δ 1, δ 2 satisfying [δ 1(x), δ 2(y)]?=?[x, y] for all x, y in a nonzero right ideal of R. This result is a natural generalization of Bell and Daif’s theorem on strong commutativity preserving derivations and a recent result by Ali and Huang. 相似文献
19.
Yongzhong Song 《BIT Numerical Mathematics》1999,39(2):373-383
Suppose Ax = b is a system of linear equations where the matrix A is symmetric positive definite and consistently ordered. A bound for the norm of the errors
k
= x– x
k of the AOR method in terms of the norms of
k
= x
k–x
k–1 and
k+1 = x
k+1–x
k and their inner product is derived. 相似文献
20.
Wolfgang Walter 《Results in Mathematics》1994,26(3-4):399-402
The functional equation $$f(x)={1\over 2}\int^{x+1}_{x-1}f(t)\ dt\ \ \ {\rm for}\ \ \ x\ \in\ {\rm R}$$ has the linear functions ?(x) = a + bx (a, b ∈ ?) as trivial solutions. It is shown that there are two kinds of nontrivial solutions, (i) ?(x) = eλi x (i = 1, 2, …), where the λi∈ ? are the fixed points of the map z ? sinh z, and (ii) C∞-solutions ? for which the values in the interval [?1,1] can be prescribed arbitrarily, but with the provision that ?(j)(? 1) = ?(j)(0) = ?(j)(1) = 0 for all j = 0, 1, 2 … 相似文献
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