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1.
本文讨论了Z[(-5)1/2]上不可分的正定Hermite型的构作.给出了所有秩为2判别式等于2的不可分的正定Hermite型.当秩n≥3时,证明了存在Z[(-5)1/2]上判别式等于2的不可分的正定Hermite型,并给出了它们的明显结构.  相似文献   

2.
本文讨论了Z[(-5)~(1/2)]上不可分的正定 Hermite型的构作.给出了所有秩为 2判别式等于2的不可分的正定Hermite型。当秩n ≥ 3时,证明了存在Z[(-5)~(1/2)]上判别式等于2的不可分的正定Hermite型,并给出了它们的明显结构.  相似文献   

3.
朱福祖 《中国科学A辑》1992,35(6):561-571
本文给出了构作Z[m1/2i]上不可分的正定幺模n秩Hermite格当m?3(mod4)时的方法.对任何自然数n,除了n=2,3,4,5(n=2,3)的例外情形,证明了存在Gauss整环Z[i](整环Z[21/2i])上不可分的正定幺模n秩正规Hermi-te格并给出它们的明显结构.又对任何n=4k(n=2k)构作了Z[i][(Z21/2i])上不可分的正定幺模n秩偶Hermite格.  相似文献   

4.
朱福祖 《中国科学A辑》2000,30(3):210-217
给出构作虚二次域Q( √-m)的整数环Rm 上的不可分解的正定Hermite型的方法 .对任意自然数n≥ 2 (n≥ 1 3或奇数n≥ 3)和不含平方因子的m =1 2k +t,k≥ 1且t∈ {1 ,7}(k≥ 1且t=2或k≥ 0且t∈ {5 ,1 0 ,1 1 }) ,存在环Rm 上n秩不可分解的正定整Hermite型 ,其判别式为 2 ,并给出它们的明显结构 .对于判别式不等于2的情况也做了相应的讨论 .  相似文献   

5.
设 R 为虚二次域 Q(-11)~(1/2)的代数整数环,C_(n,Δ_n) 为秩 n 而判别式=Δ_n 的 R上正定 Hermite 型的类数。作者应用 Hermite 约简理论确定了类数 C_(2,3)=C_(2,4)=C_(2,5)=2;C_(3,2)=C_(3,3)=3;C_(4,1)=5并给出了每一类的代表型。  相似文献   

6.
本文利用推广的邻格方法,完成了Z[(*)6]上秩4判别式1的所有正定幺模格的分类.  相似文献   

7.
虚二次域上不可分的正定Hermite型的构作   总被引:2,自引:0,他引:2  
本文给出了构作虚二次域IQ(-m)上不可分的正定整Hermite型的方法.对任意给定的自然数n,d和无平方因子的m,当m3(mod4),除了m=1时n=2,d=1;n=3,d=1,3;n=5,d=1和m=2时n=3,d=1这5个例外,证明了存在IQ(-m)上不可分的正定整Hermite格,其秩为n且判别式为d,并给出它们的明确结构.在上述5个例外情形下,不存在具有上述性质的格.  相似文献   

8.
Hermite正定对称矩阵迹的一些结果(英文)   总被引:1,自引:0,他引:1  
冯天祥  刘红霞 《数学杂志》2012,32(2):263-268
本文研究了一类Hermite正定矩阵迹的不等式问题.利用文献[2-6]中的结果以及放缩法,获得了Hermite正定矩阵迹的极值定理、杨氏不等式和贝努利不等式,并且将许多初等不等式推广到Hermite正定矩阵迹的情形.  相似文献   

9.
Hermite正定矩阵迹的几个重要不等式   总被引:2,自引:0,他引:2  
本文研究了Hermite正定矩阵迹的不等式问题.利用文献[1、2]的部分结果和矩阵恒等变形的方法,得到了关于Hermite正定矩阵迹的几个重要不等式,推广了文献[5、6]的结果  相似文献   

10.
Z[6~(1/2)]上的正定么模格的分类   总被引:1,自引:0,他引:1  
王瑞卿 《数学学报》2002,45(3):583-588
本文利用推广的邻格方法,完成了Z[ ]上秩 4判别式 1的所有正定么模格的分类.  相似文献   

11.
CONSTRUCTIONOFINDECOMPOSABLEDEFINITEHERMITIANFORMS¥ZHUFUZU(DepartmelltofMathematics,EastChinaNormalUniversitytShanghai200062,...  相似文献   

12.
We construct lattices with quadratic structure over the integers in quadratic number fields having the property that the rank of the quadratic structure is constant and equal to the rank of the lattice in all reductions modulo maximal ideals. We characterize the case in which such lattices are free. The construction gives a representative of the genus of such lattices as an orthogonal sum of “standard” pieces of ranks 1–4 and covers the case of the discriminant of the real quadratic number field congruent to 1 modulo 8 for which a general construction was not known.   相似文献   

13.
We classify even unimodular Gaussian lattices of rank 12, that is, even unimodular integral lattices of rank 12 over the ring of Gaussian integers. This is equivalent to the classification of the automorphisms τ with τ2=−1 in the automorphism groups of all the Niemeier lattices, which are even unimodular (real) integral lattices of rank 24. There are 28 even unimodular Gaussian lattices of rank 12 up to equivalence.  相似文献   

14.
This paper displays the relation between the Dynkin diagrams of rational double points on a normal quinticK3 surface with one triple point and the positive definite lattices of rank 16 with discriminant 5. Under certain conditions, the former can be obtained from the Dynkin diagrams of the latter by a succession of two elementary transformations. Supported by the National Natural Science Foundation of China.  相似文献   

15.
The Bundle Theorem is proved for geometric locally projective lattices of rank 4 which for every given line (rank 2 element) do not contain too many lines that are on a common plane (rank 3 element) with this line, but on no common point (rank 1 element). By a result of J. Kahn (Math. Z.175 (1980), 219–247), this implies that these lattices are projectively embeddable.  相似文献   

16.
Kneser's method of constructing adjacent lattices will be used to determine class numbers of unimodular positive definite hermitian lattices of rank 2 and 3 over rings of integers in some imaginary quadratic fields. The same method will also be applied in order to construct indecomposable unimodular positive definite hermitian lattices of rank 2 and 3 over almost all orders in imaginary quadratic fields, even non-maximal ones. All exceptional cases will be determined explicitly. In part supported by NSF grant DMS 8805262. I would like to thank Prof. Martin Kneser for the support and the many helpful hints I received during the work on my Diplom thesis on which this paper is based, and also Prof. T.-Y. Lam for providing me with the grant without which I would not have been able to devote part of my time to writing this paper.  相似文献   

17.
The flag Whitney numbers (also referred to as the flag f-numbers) of a geometric lattice count the number of chains of the lattice with elements having specified ranks. We give a collection of inequalities which imply all the linear inequalities satisfied by the flag Whitney numbers of rank 3 geometric lattices. We further describe the smallest closed convex set containing the flag Whitney numbers of rank 3 geometric lattices as well as the smallest closed convex set containing the flag Whitney numbers of those lattices corresponding to oriented matroids.  相似文献   

18.
王瑞卿 《数学学报》2016,59(3):295-302
构作了有理函数域F_(19)(x)上秩3到6的不可分格,回答了Gerstein关于整体函数域上是否存在秩5的不可分格的问题.  相似文献   

19.
段俊生 《数学杂志》2006,26(5):478-484
研究了交换半环上矩阵的秩和坡上矩阵的可逆条件.利用Beasley的引理以及不变式,获得了交换半环上正则矩阵的行秩、列秩与Schein秩三者相等,以及坡上矩阵可逆的充要条件.推广模糊代数和分配格上矩阵的结果.  相似文献   

20.
We show that twin building lattices are undistorted in their ambient group; equivalently, the orbit map of the lattice to the product of the associated twin buildings is a quasi-isometric embedding. As a consequence, we provide an estimate of the quasi-flat rank of these lattices, which implies that there are infinitely many quasi-isometry classes of finitely presented simple groups. Finally, we describe how non-distortion of lattices is related to the integrability of the structural cocycle.  相似文献   

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