共查询到19条相似文献,搜索用时 203 毫秒
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杨学枝老师在文[1]中提出的猜想21如下:
设xi∈-R,i=1,2,…,n,记s1=η∑xi=1,sn-1=x2x3…xn+x1x3…xn+…+x1x2…xn-1,sn=x1x2…xn,则
sn1-(n-1)n-1 s1 sn-1+n2[(n-1)n-1-nn-2]Sn≥0,①
当且仅当x1=x2-…=xn时取等号.
笔者探究发现①式取等号成立的充要条件应该是:x1=x2=…=xn,或x1=x2=…=xn-1,xn=0. 相似文献
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杨克昌、陈培德两老师在贵刊文[1]给出如下:定理1 设0≤d≤2,xi>0,1≤i≤n,则max1≤i≤n{xi}(x1 (1 d)x2 … (1 (n-1)d)xn)≥(n-1)d 22n(x1 x2 … xn)2等号成立当且仅当x1=x2=…=xn.笔者读后深感此不等式很奇妙,并思之此定理有其对偶的形式,即有定理2 设0≤d≤2,xi>0,1≤i≤n,则min1≤i≤n{xi}(x1 (1 d)x2 … (1 (n-1)d)xn)≤(n-1)d 22n(x1 x2 … xn)2(1)等号成立当且仅当x1=x2=…=xn.证明的方法同文[1]证 视(1)式左边减去右边所得的差为d的函数,记作g(d).显见g(d)是一个线性函数.所以为证g(d)在整个区间[0,2]上非正,只要证g(d)在区间端… 相似文献
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对于函数F(x1,x2,…,xn)=|a1x1 a2x2 … anxn A|,由绝对值的意义知F(x1,x2,…,xn)≥0.特别,当ai,xi,A∈Z(i=1,2,…,n)时,该函数有更精确的下界,本文将给出这个结论.定理设F(x1,x2,…,xn)=|ni=1aixi A|,ai,xi,ki,A,m∈Z,(a1,a2,…,an)=d,ai=kid,(k1,k2,…,kn)=1,A=md r,0≤r相似文献
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对偶余模函子()°和余反射余模 总被引:3,自引:0,他引:3
本文给出对偶余模M°的结构刻划及()°作为逆变函子的左正合性.同时引入余反射余模描述余反射余代数,由此研究余反射余代数的同调性质,证明当char(F)=0时,F[x1,...,xn]°上的Serre猜测是成立的,即F[x1,...,xn]°的有限余生成内射余模均为余自由的. 相似文献
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对于函数F(x1,x2,…,xn)=|α1x1 α2x2 … αnxn A|,由绝对值的意义知F(x1,x2,…,xn)≥0,特别,当αi,xi,A∈Z(i=1,2,…,n)时,该函数有更精确的下界,本文将给出这个结论。 相似文献
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[1 ]给出复数域C上多元多项式环 C[x1 ,x2 ,… ,xn]的一类整除性定理 ,本文把它推广为任意代数闭域 k上多元多项式环 k[x1 ,x2 ,… ,xn]的情形 . 相似文献
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Let D [d] =(a,b/F) a quaternion divisior algebra over a field F of characteristic ? 2. Denote 1, i, j , k the basis of D, such that i2[d] n, j2[d] b, ij [d] -ji [d] k and A :D → D the involution given by i [d] -i, j [d] j (and k [d] k). In [LE] D. LEWIS asks the following question :Does there exist a quadratic Pfister form [S p. 721 [d] such that the hermitian form [d] [d] D is isotropic over (D, [d]) but not hyperbolic &; In this note, we show that the answer of this question is negative, so that the hermitien level [§I], when it is finite, of (D, A) is a power of two. This result holds for quaternion algebras with standard involution [LE]. 相似文献
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标准分层代数是拟遗传代数的推广,其性质和理论意义受到人们的重视.在本文中,设A是域k上的标准分层代数,我们从特征模的角度,对A的多项式代数A[x]上的滤链维数进行了研究,得到了一些有意义的结果. 相似文献
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A. A. Tuganbaev 《Journal of Mathematical Sciences》1995,75(3):1750-1753
It is proved that the distributiveness of the right ideals lattice for a quaternion algebra over a commutative ring A is equivalent
to the following property: the equation x2+y2+z2=0 is uniquely solvable in the field A/M for any maximal ideals M of A, the lattice of the ideals of A being distributive.
Bibliography: 5 titles.
Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 17, pp. 209–214, 1994. 相似文献
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苏育才 《中国科学A辑(英文版)》2003,46(3):346-354
A class of the associative and Lie algebras A[D] = A F[D] of Weyl type are studied, where A is a commutative associative algebra with an identity element over a field F of characteristic zero, and F[D] is the polynomial algebra of a finite dimensional commutative subalgebra of locally finite derivations of A such that A is D-simple. The derivations of these associative and Lie algebras are precisely determined. 相似文献
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Helmut Röhrl 《manuscripta mathematica》1978,25(4):359-390
In [3] it was shown that a polynomial of degree n with coefficients in an associative division algebra, which is d-dimensional over its center, has either infinitely many or at most nd zeros. In this paper we raise the same question for arbitrary m-ary F-algebras A which are d-dimensional over the algebraically closed field F. Our main result states that in the affine space of m-ary algebras of dimension d there is a non-empty Zariski-open set whose elements A have the following property: in the space of polynomial of precise degree n with coefficients in A there is a non-empty Zariski-open set whose elements have precisely nd zeros. It is shown that all simple algebras, all semi-simple associative algebras, all semisimple Jordan algebras (char F2), all semi-simple Lie algebras (char F=0), and the generic algebra possess this property. 相似文献
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设HF为域F上广义四元数可除代数,其中charF≠2.应用伴随矩阵与矩阵表示方法,本文得到HF上矩阵方程∑ki=0AiXBi=E有解或有唯一解的几个充要条件,并且给出了几个解的公式. 相似文献
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Otto Körner 《manuscripta mathematica》1985,52(1-3):203-225
Let M be any order of a quaternion algebra Q over a local field F. The group Mx of units and the central Picard group Picent (M) of M are investigated. The group index (Lx:Mx) and, if F is of characteristic 2, also the norms of all primitive ideals of M and the order of Picent (M) are determined explicitly, where L denotes any maximal order of Q containing M. Applications of these results to local densities of ternary quadratic forms and to class numbers and type numbers of global quaternion orders are indicated. 相似文献
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Abraham Broer 《Transformation Groups》2006,11(4):551-574
Let
be a graded polynomial
algebra over a field k, such that each variable is homogeneous of positive degree. No restrictions are made with respect to
the field. Let the finite group G act on A by graded algebra automorphisms and denote the subalgebra of invariants by B. In
this paper the various "different ideals" of the extension
are studied that define the ramification locus. We prove, for example, that the subring of invariants is itself a polynomial
ring if and only if the ramification locus is pure of height one. Here the ramification locus is defined by either the Kahler
different, the Noether different or the Galois different. As a consequence we prove that the invariant ring is itself a polynomial
ring if and only if there are invariants
whose Jacobian determinant does not vanish and is of degree δ, where δ is the degree of the Dedekind different. Using this
criterion we give a quick proof of Serre's result that if the invariant ring is a polynomial algebra, then the group is generated
by generalized reflections. 相似文献