Triangularizing matrices over GF(2) by congruence

Necessary and sufficient conditions are presented for a square matrix over GF(2) to be triangulable by congruence.     

具有逆断面的正则半群的同余的表示

具有道断面S°的正则半群可表示为有Saito's结构的半群W（I，S°，Λ，*，α，β）.我们利用由I，S°和Λ上的同余构成的所谓同余聚抽象地表示这类半群上的同余，进而给出了这类半群的同态象的构造法．     

一类满足可补性质的双重Stone代数

该文构造了一个从布尔代数范畴到满足可补性质的双重Ｓｔｏｎｅ 代数范畴的函子，并证明了这个函子有一个等价的左伴随函子．     

关于Euler数的一个问题的解决

本文证明了:对任何素数p≡5(mod 8);有 E(p-1)/2≠0(mod p),这里E_(2n)是Euler数。     

对合Quantale同余关系

给出对合Quantale同余的概念,得到了对合Quantale同余的一些性质,讨论了对合Quantale同余与同态之间的关系,最后给出了对合Quantale乘积上的同余关系的结构。     

A cycle lemma for permutation inversions

In this paper we study some properties of the inversion statistic. Some enumerative results concerning the permutations of the multiset {x₁^m₁,x₂^m₂} with respect to the inversion parameter are established and it is shown that these depend on gcd(m₁,m₂). Using a “cycle lemma”, a combinatorial proof of the results is given. Moreover, some applications to the Gaussian binomial coefficient are illustrated.     

Leibniz代数上的粗糙集

把粗糙集理论方法应用到Leibniz代数上,定义了Leibniz代数上的同余关系,给出了Leibniz代数的粗糙子代数和粗糙理想等概念,研究了Leibniz代数上粗糙集在同态映射下的若干性质.     

Matrices that are self-congruent only via matrices of determinant one

Đocović and Szechtman [D.Ž. Đocović, F. Szechtman, Characterization of bilinear spaces with unimodular isometry group, Proc. Amer. Math. Soc. 133 (2005) 2853–2863] considered a vector space V endowed with a bilinear form. They proved that all isometries of V over a field of characteristic not 2 have determinant 1 if and only if V has no orthogonal summands of odd dimension (the case of characteristic 2 was also considered). Their proof is based on Riehm’s classification of bilinear forms. Coakley et al. [E.S. Coakley, F.M. Dopico, C.R. Johnson, Matrices with orthogonal groups admitting only determinant one, Linear Algebra Appl. 428 (2008) 796–813] gave another proof of this criterion over and using Thompson’s canonical pairs of symmetric and skew-symmetric matrices for congruence. Let M be the matrix of the bilinear form on V. We give another proof of this criterion over using our canonical matrices for congruence and obtain necessary and sufficient conditions involving canonical forms of M for congruence, of (M^T,M) for equivalence, and of M^-TM (if M is nonsingular) for similarity.     

A generalization of Cohen- Eisenstein series and Shimura liftings and some congruences between Cusp forms and Eisenstein series

In this paper we introduce some modular forms of half-integral weight on congruence group Г_o(4N) withN an odd positive integer which can be viewed as a natural generalization of Cohen-Eisenstein series. Using these series, we can prove that the restriction of Shimura lifting on Eisenstein spaceE _k+1/2 ⁺ (4N,χl) gives an isomorphism fromE _k+1/2 ⁺ (4N,χl) toE _2k(N). We consider some congruence relationships between modular forms in use of Shimura lifting.     

Kleene代数的诱导子代数及理想

由于逻辑学研究的需要 ,Kleene代数理论的重要性已越来越明显 .本文主要研究了Kleene代数的子代数及理想的一些性质 ,得到了一些比较好的结果 .