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1.
Let μ be a nonnegative Radon measure on R d which satisfies the growth condition μ(B(x,r)) ≤ C0rn for all x ∈Rd and r >0,where C0 is a fixed constant and 0相似文献
2.
Vincenzo de Filippis 《数学学报(英文版)》2009,25(12):1965-1974
Let R be a prime ring, L a non-central Lie ideal of R and g a non-zero generalized derivation of R. If g acts as a Jordan homomorphism on L, then either g(x) = x for all x ∈ R, or char(R) = 2, R satisfies the standard identity s4(x1, x2, x3, x4), L is commutative and u2 ∈ Z(R), for any u C L. We also examine some consequences of this result related to generalized derivations which act as Jordan homomorphisms on the set [I, I], where I is a non-zero right ideal of R. 相似文献
3.
《数学季刊》2020,(2)
Let R be a prime ring with characteristic different from two, d a derivation of R, L a noncentral Lie ideal of R, and a ∈ R. In the present paper it is showed that if a(d(u~m) ± u~m)n= 0 for all u ∈ L, where m,n are fixed positive integers, then a = 0 unless R satisfies s_4, the standard polynomial identity in four variables. 相似文献
4.
Let R be a prime ring, L a noncentral Lie ideal and σ a nontrivial automorphism of R such that usσ(u)ut= 0 for all u ∈ L, where s, t are fixed non-negative integers. If either char R s + t or char R = 0, then R satisfies s4, the standard identity in four variables. We also examine the identity(σ([x, y])-[x, y])n=0 for all x, y ∈ I, where I is a nonzero ideal of R and n is a fixed positive integer. If either char R n or char R = 0, then R is commutative. 相似文献
5.
McCoy环的扩张(英文) 总被引:1,自引:1,他引:0
A ring R is said to be right McCoy if the equation f(x)g(x)=0,where f(x)and g(x)are nonzero polynomials of R[x],implies that there exists nonzero s∈R such that f(x)s=0.It is proven that no proper(triangular)matrix ring is one-sided McCoy.It is shown that for many polynomial extensions,a ring R is right McCoy if and only if the polynomial extension over R is right McCoy. 相似文献
6.
Yu WANG Hong YOU 《数学学报(英文版)》2006,22(6):1715-1720
This note proves that, if R is a prime ring of characteristic 2 with d a derivation of R and L a noncentral Lie ideal of R such that [d(u),u]^n is central, for all u ∈ L, then R must satisfy s4, the standard identity in 4 variables. The case where R is a semiprime ring is also examined by the authors. The results of the note improve Carini and Filippis's results. 相似文献
7.
Throughout,R will be semiprime ring,Qmr=Qmr(R) the maximal right quotient ringof R,and C=Z(Qmr) the extended centroid of R(see[1 ,Chapter2 ] for details) . In [2 ] ,Bresar,M.discussed the identity of derivations in a prime ring,and provedthat if nonzero derivations d and g of R satisfy d(x) g(y) =g(x) d(y) for all x,y∈R,then there exists aλ in C such thatg(x) =λd(x) for all x∈ R.Itis natural to ask whatresults can be obtained if d(x) g(x) =g(x) d(x) for all x∈ R.In[3 ] ,Bresa… 相似文献
8.
In this paper we proved two theorems which are generalizations of Goldie’sTheorem, Definition 1.A ring R is said to be a right G-ring,if R satisfies (i)For any nonezero left ideal L of R,there exists 0≠x∈L,for any S,t∈R, st≠0,xt≠0 imply sxt≠0. (ii)For any x∈R,the right Goldie’s dimension of xR is finite. Definition 2.Let Δ be a division ring and N be a veetor space over Δ,a 相似文献
9.
REGULARIZATION OF AN ILL-POSED HYPERBOLIC PROBLEM AND THE UNIQUENESS OF THE SOLUTION BY A WAVELET GALERKIN METHOD
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We consider the problem K(x)u xx = u tt , 0 < x < 1, t ≥ 0, with the boundary condition u(0,t) = g(t) ∈ L 2 (R) and u x (0, t ) = 0, where K(x) is continuous and 0 < α≤ K (x) < +∞. This is an ill-posed problem in the sense that, if the solution exists, it does not depend continuously on g. Considering the existence of a solution u(x, ) ∈ H 2 (R) and using a wavelet Galerkin method with Meyer multiresolution analysis, we regularize the ill-posedness of the problem. Furthermore we prove the uniqueness of the solution for this problem. 相似文献
10.
Entropy and renormalized solutions for nonlinear elliptic problem involving variable exponent and measure data
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Mohamed Badr Benboubker Houssam Chrayteh Mostafa El Moumni Hassane Hjiaj 《数学学报(英文版)》2015,31(1):151-169
We give an existence result of entropy and renormalized solutions for strongly nonlinear elliptic equations in the framework of Sobolev spaces with variable exponents of the type:-div(a(x, u, u) + φ(u)) + g(x, u, u) = μ, where the right-hand side belongs to L1(Ω) + W-1,p(x)(Ω),-div(a(x, u, u)) is a Leray–Lions oper- ator defined from W-1,p(x)(Ω) into its dual and φ∈ C0(R, RN). The function g(x, u, u) is a non linear lower order term with natural growth with respect to |u| satisfying the sign condition, that is,g(x, u, u)u ≥ 0. 相似文献
11.
L. M. Samoilov 《Mathematical Notes》1999,65(2):208-213
In the paper, trinomial identities of associative algebras over an infinite field are considered (in general, the algebras
may have no unit), i.e., identities of the formα
m
1+β
m
2+γ
m
3=0, where α, β, and γ are scalars andm
1,m
2, andm
3 are different monomials. It is shown that any nontrivial identity if this kind implies a semigroup identity. The algebras
with trinomial identities are characterized in the language of varieties.
Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 254–260, February, 1999. 相似文献
12.
《代数通讯》2013,41(10):5003-5010
Abstract Let R be a prime ring of characteristic different from 2, d a non-zero derivation of R, I a non-zero right ideal of R, a ∈ R, S 4(x 1,…, x 4) the standard polynomial in 4 variables. Suppose that, for any x, y ∈ I, a[d([x, y]), [x, y]] = 0. If S 4(I, I, I, I)I ≠ 0, then aI = ad(I) = 0. 相似文献
13.
14.
J. Płonka 《Southeast Asian Bulletin of Mathematics》2002,25(3):495-502
We consider algebras of a type , without nullary fundamental operation symbols. A structural property p of an identity of type is hereditary if for every set I of identities of type having the property p every consequence of I (derived identity) has the property p. An algebra
of type we call characteristic for a hereditary property p if for every variety V of type we have:
V if and only if every identity from Id(V) has the property p. In this paper we show minimal characteristic algebras for several hereditary properties, e.g., to be regular, to be normal, etc.1991 Mathematics Subject Classification
08B05 相似文献
15.
This paper is devoted to the counting of j-chains of lattice-point poset. The incidence function and two basic enumerators associated with it are introduced and evaluated. Our results contain a lot of combinatorial sums. 相似文献
16.
In this paper we prove that for fixed positive integers α, β, m and m ≥ 2 the equation (?) holds for n = 2 only when m = 2, α = 3 and β = 1, which is another improvement of LeVeque's result, different from Yu's. 相似文献
17.
本文利用初等刀法简捷地推广了Paule的结果,从而得到了一系列多重Rogers-Ramanujan恒等式. 相似文献
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20.
Let
be an algebraic algebra over an infinite field K and let
(
) be its group of units. We prove a stronger version of Hartley's conjecture for
, namely, if a Laurent polynomial identity (LPI, for short) f = 0 is satisfied in
(
), then
satisfies a polynomial identity (PI). We also show that if
is non-commutative, then
is a PI-ring, provided f = 0 is satisfied by the non-central units of
. In particular,
is locally finite and, thus, the Kurosh problem has a positive answer for K-algebras whose unit group is LPI. Moreover, f = 0 holds in
(
) if and only if the same identity is satisfied in
. The last fact remains true for generalized Laurent polynomial identities, provided that
is locally finite. 相似文献