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81.
The discrete logarithm problem in various finite abelian groups is the basis for some well known public key cryptosystems. Recently, real quadratic congruence function fields were used to construct a public key distribution system. The security of this public key system is based on the difficulty of a discrete logarithm problem in these fields. In this paper, we present a probabilistic algorithm with subexponential running time that computes such discrete logarithms in real quadratic congruence function fields of sufficiently large genus. This algorithm is a generalization of similar algorithms for real quadratic number fields.
82.
Pawel M. Idziak 《Transactions of the American Mathematical Society》1997,349(3):903-934
For every finitely generated, congruence modular variety of finite type we find a finite family of finite rings such that the variety is finitely decidable if and only if is congruence permutable and residually small, all solvable congruences in finite algebras from are Abelian, each congruence above the centralizer of the monolith of a subdirectly irreducible algebra from is comparable with all congruences of , each homomorphic image of a subdirectly irreducible algebra with a non-Abelian monolith has a non-Abelian monolith, and, for each ring from , the variety of -modules is finitely decidable.
83.
G. Grätzer, H. Lakser, and E. T. Schmidt proved that every finite distributive lattice D with n join-irreducible elements can be represented as the congruence lattice of a lattice L with O(n2) elements. G. Grätzer, I. Rival, and N. Zaguia gave kn, < 2, as a lower bound for the size of such a lattice L; a sharper form, 1/64(n/log2n)2, of this result was given by Y. Zhang.In this note, we apply a recent result of R. Freese, to obtain 1/16 n2/log2n as a lower bound. We also give a direct proof of Freese's result. 相似文献
84.
Roger C. Alperin 《Proceedings of the American Mathematical Society》1996,124(10):2935-2941
We classify the normal subgroups of of index less than 960; they are all congruence subgroups.
85.
On ideals and congruences in bcc-algebras 总被引:10,自引:0,他引:10
We introduce a new concept of ideals in BCC-algebras and describe connections between such ideals and congruences. 相似文献
86.
Generalized Bicyclic Semigroups and Jones Semigroups 总被引:1,自引:0,他引:1
In this paper, we consider the generalized bicyclic semigroups Bn = a, b | anb = 1 and the Jones semigroups An = a, b | an+1b = a. They are the generalizations of the bicyclic semigroup B = a, b | ab = 1 and its analogous semigroup A = a, b | a2b = a discovered by P.R., Jones in 1987. The word problem for these kinds of semigroups is solved. It is proved that, for n 2, Bn are bisimple right inverse but not inverse semigroups and that the semigroup C = a, b | a2b = a, ab2 = b is the smallest idempotent-free homomorphic image of An. Moreover, we also prove that An and Am are mutually embeddable but not isomorphic with each other if n m. As a consequence, different kind of
-nontrivial [0-]simple semigroups without idempotents are discussed.AMS 1991 Subject Classification: primary 20M10 secondary 20M05.Supported by NNSF of China (19671063) and KSRF of Sichuan Education Committee ([1999]127). 相似文献
87.
伪补分配格的同余理想与同余关系 总被引:5,自引:1,他引:4
王尊全 《纯粹数学与应用数学》2001,17(4):363-367
L是完备的伪补分配格,I是L的同余理想,本文得到以下结果:⑴θ是L的以I为核的最大同余关系的条件。⑵L的以I为核的同余关系是唯一的充分必要条件。⑶L的同余理想与同余关系之间有一一对应关系的充分必要条件。 相似文献
88.
Bjorn Schellenberg 《International Journal of Mathematical Education in Science & Technology》2013,44(3):311-321
A set of axioms for classical absolute geometry is proposed that is accessible to students new to axioms. The metric axioms adopted are the ruler axiom, triangle inequality and the bisector axiom. Angle measure is derived from distance, and all properties needed to establish a consistent system are derived. In particular, the SAS congruence theorem is proved. The proofs are broken into many small steps suitable for the target audience. Some explorations with geometry drawing programmes are shown. 相似文献
89.
Let G be a simple connected graph and L(G) be its Laplacian matrix. In this note, we prove that L(G) is congruent by a unimodular matrix to its Smith normal form if and only if G is a tree. 相似文献
90.
Tian-Gang Lei 《Linear and Multilinear Algebra》2013,61(4):411-427
The earliest congruence numerical range was introduced by Thompson in 1980. Since then, congruence numerical ranges and their radii have been studied by some authors. The purpose of this article is to discuss several aspects of this subject. We survey some known results and propose some problems for furthur study. A few new results are also presented. 相似文献