Bernoulli数模2r和3r的同余式

设{Bn}为Bernoulli数,m、n为自然数,本文证明了同余式(2-22n)B2n≡1-4n ∑mk=1(2n)/(2k)24kB2k (mod 24m 3)与(3-32n)B2n≡2-6n 2∑mk=1(2n)/(2k)32kB2k (mod 32m 1).取m=1,2,得到[5]中宣布的(2-22n)B2n(mod 27)与(3-32n)B2n(mod 35)的简单同余式.     

正则带的半格结构

Petrich解决了一般带的构造定理（见[1]或[2]），在此基础上，我们将证明正则带（满足等式axya=axaya的带）的一些特征，并给出一个带为正则带或右似正规带（满足等式xya=xaya的带）的充分必要条件，这些结果是Yamada和Kimura的关于正规带（满足等式axya=ayxa的带）的结果的推广，正规带被他们描述为矩形带的强半格（见[1]或[3]）。     

关于序半群的半格同余

Ｎ．Ｋｅｈａｙｏｐｕｌｕ教授在「１」中提出“ｐ０－半群上的半格同余‘Ｎ’是否为去掉最小半格同余”的问题。本文引进半格同余ｎ,证明存在ｐ０－半群Ｓ,Ｓ,上的半格同余ｎ∩→上的半格同余ｎ∩→Ｎ,给出该问题否定回答。     

双循环半群上的同余

双循环半群在逆半群的研究中起着重要的作用,对此类半群上的同余关系进行了探讨,从而得到一些重要的结论.     

正则半群上的完全单半群同余

研究了正则半群上的完全单半群同余,给出了这类同余的若干等价刻画,证明了≤*是任意正则半群上的最小完全单半群同余,(≤∪≤-1)t是任意局部逆半群上的最小完全单半群同余,是任意逆半群上的最小群同余.     

正则半群上与格林关系有关的同余

讨论正则半群上与格林关系有关的同余生成的格,研究这个格的Hasse图的几种退化情形,然后确定逆半群和两类特殊的完全正则半群上与格林关系有关的同余所生成的同余格.     

超富足半群及其子类

借助半群的Malcev积和公理化条件,对超富足半群及其子类进行了刻画,给出了超富足半群及其子类的若干特征.     

Newton polyhedra, unstable faces and the poles of Igusa's local zeta function

In this paper we examine when the order of a pole of Igusa's local zeta function associated to a polynomial is smaller than ``expected'. We carry out this study in the case that is sufficiently non-degenerate with respect to its Newton polyhedron , and the main result of this paper is a proof of one of the conjectures of Denef and Sargos. Our technique consists in reducing our question about the polynomial to the same question about polynomials , where are faces of depending on the examined pole and is obtained from by throwing away all monomials of whose exponents do not belong to . Secondly, we obtain a formula for Igusa's local zeta function associated to a polynomial , with unstable, which shows that, in this case, the upperbound for the order of the examined pole is obviously smaller than ``expected'.

     

Powers of Euler's Product and Related Identities

Ramanujan's partition congruences can be proved by first showing that the coefficients in the expansions of (q; q) ^r satisfy certain divisibility properties when r = 4, 6 and 10. We show that much more is true. For these and other values of r, the coefficients in the expansions of (q; q) ^r satisfy arithmetic relations, and these arithmetic relations imply the divisibility properties referred to above. We also obtain arithmetic relations for the coefficients in the expansions of (q; q) ^r (q ^t; q ^t) ^s , for t = 2, 3, 4 and various values of r and s. Our proofs are explicit and elementary, and make use of the Macdonald identities of ranks 1 and 2 (which include the Jacobi triple product, quintuple product and Winquist's identities). The paper concludes with a list of conjectures.     

Complete Congruences on the Lattice of Rees–Sushkevich Varieties

We study the lattice ?(RS_n) of subvarieties of the variety of semigroups generated by completely 0-simple semigroups over groups with exponent dividing n, with a particular focus on the lattice ??(RS_n) consisting of those varieties that are generated by completely 0-simple semigroups. The sublattice of ??(RS_n) consisting of the aperiodic varieties is described and several endomorphisms of ?(RS_n) considered. The complete congruence on ??(RS_n) that relates varieties containing the same aperiodic completely 0-simple semigroups is considered in some detail.