正规密码(H)-富足半群

将Green关系推广到Green～-关系。给出了密码^ ～ H-富足半群的半格分解,利用此分解,证明了^ ～ H-富足半群为正规密码^H-富足半群当且仅当它是完全^ ～ H-单半群的强半格.     

The distribution of solutions of the congruence

For a cube of size , we obtain a lower bound on so that is nonempty, where is the algebraic subset of defined by

a positive integer and an integer not divisible by . For we obtain that is nonempty if , for we obtain that is nonempty if , and for we obtain that is nonempty if . Using the assumption of the Grand Riemann Hypothesis we obtain is nonempty if .

     

Faces of a Hyperplane Arrangement Enumerated by Ideal Dimension, with Application to Plane, Plaids, and Shi

The ideal dimension of a real affine set is the dimension of the intersection of its projective topological closure with the infinite hyperplane. We obtain a formula for the number of faces of a real hyperplane arrangement having given dimension and ideal dimension. We apply the formula to the plane, to plaids, which are arrangements of parallel families in general position, and to affinographic arrangements. We compare two definitions of ideal dimension and ask about a complex analog of the enumeration.     

Congruences for degenerate number sequences

The degenerate Stirling numbers and degenerate Eulerian polynomials are intimately connected to the arithmetic of generalized factorials. In this article, we show that these numbers and similar sequences may in fact be expressed as p-adic integrals of generalized factorials. As an application of this identification we deduce systems of congruences which are analogues and generalizations of the Kummer congruences for the ordinary Bernoulli numbers.     

Congruences involving generalized central trinomial coefficients

For integers b and c the generalized central trinomial coefficient Tn(b,c)denotes the coefficient of xnin the expansion of(x2+bx+c)n.Those Tn=Tn(1,1)(n=0,1,2,...)are the usual central trinomial coefficients,and Tn(3,2)coincides with the Delannoy number Dn=n k=0n k n+k k in combinatorics.We investigate congruences involving generalized central trinomial coefficients systematically.Here are some typical results:For each n=1,2,3,...,we have n-1k=0(2k+1)Tk(b,c)2(b2-4c)n-1-k≡0(mod n2)and in particular n2|n-1k=0(2k+1)D2k;if p is an odd prime then p-1k=0T2k≡-1p(mod p)and p-1k=0D2k≡2p(mod p),where(-)denotes the Legendre symbol.We also raise several conjectures some of which involve parameters in the representations of primes by certain binary quadratic forms.     

环的弱正则性

本文给出了环的弱正则性的一个充要条件，还讨论了Ｍｕｎｎ环的弱正则性．最后对环的半格和及补半格和，给出了弱正则性的刻画．     

On ℘-regular semigroups having regular *-transversals

Our aim is to investigate the properties and structure of the ℘-regular semigroups having regular *-transversals. We first give two kinds of definitions for regular *-transversals and prove that they are equivalent. A condition for two regular *-transversals of a ℘-regular semigroup to be isomorphic is given. The *-congruences on the ℘-regular semigroups having regular *-transversals are characterized by using the *-congruence triples. In particular, we describe the idempotent separating congruences and the group congruences on such ℘-regular semigroups.     

Relative principal congruences in congruence-modular quasivarieties

The problem of definability of relative principal congruences in relatively congruence modular (RCM) quasivarieties is investigated. The RCM quasivarieties are characterized in terms of parameterized families of finite sets of pairs of terms which define relative principal congruences. Received April 24, 1995; accepted in final form March 2, 1998.     

Decomposability of free Łukasiewicz implication algebras

?ukasiewicz implication algebras are {→,1}-subreducts of Wajsberg algebras (MV-algebras). They are the algebraic counterpart of Super-?ukasiewicz Implicational logics investigated in Komori, Nogoya Math J 72:127–133, 1978. The aim of this paper is to study the direct decomposability of free ?ukasiewicz implication algebras. We show that freely generated algebras are directly indecomposable. We also study the direct decomposability in free algebras of all its proper subvarieties and show that infinitely freely generated algebras are indecomposable, while finitely free generated algebras can be only decomposed into a direct product of two factors, one of which is the two-element implication algebra.     

可迁格序置换群的凸同余

给出了可迁格序置换群的凸同余与块所决定的可迁格序置换群的分类，讨论了可迁格序置换群的凸同余和块的性质以及它们之间的一些关系．