共查询到20条相似文献,搜索用时 15 毫秒
1.
Wai Kiu Chan Byeong-Kweon Oh 《Proceedings of the American Mathematical Society》2004,132(6):1567-1573
An integral quadratic form is said to be almost regular if globally represents all but finitely many integers that are represented by the genus of . In this paper, we study and characterize all almost regular positive definite ternary quadratic forms.
2.
Detlev W. Hoffmann 《manuscripta mathematica》1991,71(1):399-429
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
3.
Fuzu Zhu 《数学学报(英文版)》1995,11(3):291-299
In this paper, for any given natural numbersn anda, we can construct explicitly positive definite indecomposable integral Hermitian forms of rankn over
with discriminanta, with the following ten exceptions:n=2,a=1, 2, 4, 10;n=3,a=1, 2, 5;n=4,a=1;n=5,a=1; andn=7,a=1. In the exceptional cases there are no forms with the desired properties. The method given here can be applied to solving the problem of constructing indecomposable positive definite HermitianR
m
-lattices of any given rankn and discriminanta, whereR
m
is the ring of algebraic integers in an imaginary quadratic field
with class number unity. 相似文献
4.
Zhu Fuzu 《数学学报(英文版)》1994,10(2):113-120
For any natural numbersm andn≥17 we can construct explicitly indecomposable definite unimodular normal Hermitian lattices of rankn over the ring of algebraic integersR
m
in an imaginary quadratic field
. It is proved that for anyn (in casem=11, there is one exceptionn=3) there exist indecomposable definite unimodular normal HermitianR
15(R
11)-lattices of rankn, and we exhibit representatives for each class. In the exceptional case there are no lattices with the desired properties.
The method given in this paper can solve completely the problem of constructing indecomposable definite unimodular normal
HermitianR
m
-lattices of any rankn for eachm.
Dedicated to the memory of Prof. Lee Hwa-Chung. 相似文献
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Gerhard Behrendt 《Monatshefte für Mathematik》1987,103(2):77-83
We consider a setX with a finite totally ordered setE of equivalence relations onX. We describe the automorphism group of this system, that is, the group of all those permutations ofX that leave each relation inE invariant. 相似文献
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N. Ya. Medvedev 《Algebra and Logic》1999,38(2):93-106
It is proved that there exist orderable groups having exactly 6 and 14 distinct linear orders. For any natural number k, we construct examples of orderable groups on which 2(4k+3) linear orders are defined. Supported by RFFR grant No. 96-01-00088. Translated fromAlgebra i Logika, Vol. 38, No. 2, pp. 176–200, March–April, 1999. 相似文献
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We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number of solutions to n=x
2+Ny
2 for a squarefree integer N.
相似文献
17.
Wenxue Huang 《Linear and Multilinear Algebra》1996,40(4):303-309
Let A be a linear (i.e., finite-dimensional) associative algebra with unity defined over K, an algebraically closed field. Then A with respect to its multiplication is an algebraic monoid over k, denoted by AM, and with respect to the the bracket forms a Lie algebra over K, denoted by AL. The following theorem is established AM is nilpotent as an algebraic monoid (equivalentlyAL is so as a Lie algebra) if and only if the set of idempotents of A is finite if and only if all irreducible closed submonoids of codimension 1 are nilpotent. 相似文献
18.
Michał Walicki 《Discrete Mathematics》2019,342(2):473-486
According to Richardson’s theorem, every digraph without directed odd cycles that is either (a) locally finite or (b) rayless has a kernel (an independent subset with an incoming edge from every vertex in ). We generalize this theorem showing that a digraph without directed odd cycles has a kernel when (a) for each vertex, there is a finite set separating it from all rays, or (b) each ray contains at most finitely many vertices dominating it (having an infinite fan to the ray) and the digraph has finitely many ends. The restriction to finitely many ends in (b) can be weakened, admitting infinitely many ends with a specific structure, but the possibility of dropping it remains a conjecture. 相似文献
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A.‐H. Nokhodkar 《Mathematische Nachrichten》2019,292(10):2294-2299
Quadratic descent of hermitian and skew hermitian forms over division algebras with involution of the first kind in arbitrary characteristic is investigated and a criterion, in terms of systems of quadratic forms, is obtained. A refined result is also obtained for hermitian (resp. skew hermitian) forms over a quaternion algebra with symplectic (resp. orthogonal) involution. 相似文献