SIMPLE OCKHAM ALGEBRAS

An algeber L is said to be simple, if its congruence lattice Con L reduces to the 2-elementchain {ω,v}. This paper describes the structure of finite simple Ockham algebras.     

The Self-conjugate Maximal Surfaces in L~(3*)

in this note we study the maximal surfaces which are congruent with theirconjugate ones in L3, and give a criterion for this kind of surfaces and some examples.     

One-cusped congruence subgroups of Bianchi groups

We show that there are only finitely many maximal congruence subgroups of the Bianchi groups such that the quotient by has only one cusp.     

Linear mappings on symmetry classes of tensors

In this paper we give a survey of results concerning linear mappings on symmetry classes of tensors that preserve decomposable elements and its related topic about linear mappings on spaces of matrices that preserve a fixed rank.     

Zorn's Matrices and Finite Index Subloops#

Zorn's Algebra ?(R) has a multiplicative function called determinant with properties similar to the usual one. The set of elements in ?(R) with determinant 1 is a Moufang loop that we will denote by IΓ. In our main result we prove that if R is a Dedekind algebraic number domain that contains a unit of infinite order, each finite index subloop ?, such that IΓ has the weak Lagrange property relative to ?, is a congruence subloop.     

带逆断面的正则半群上的强模糊同余

带逆断面的正则半群是一类重要的正则半群.就带逆断面的正则半群类引入强模糊同余的概念,进而用所谓的强模糊同余三元组抽象地刻画带逆断面的正则半群上的强模糊同余.     

Representation of congruences on regular semigroups with inverse transversals

For a regular semigroup with an inverse transversal, we have Saito’s structureW(I,S ^o, Λ, *, {α, β}). We represent congruences on this kind of semigroups by the so-called congruence assemblage which consist of congruences on the structure component partsI,S ^o and Λ. The structure of images of this type of semigroups is also presented. This work is supported by Natural Science Foundation of Guangdong Province     

THE FUNCTION dk（n） ATCONSECUTIVE INTEGERS

51.IntroductionForallpositiveintegersk32,wedefinethefunctionsdk(n)bytheidentityWeknowthatdk(n)isamultiplicativefunction.Ifthestandardformofnisn=p?'p:'tthenwehavethefollowingformu1aTheaboveformulascanbefoundin[4].Inl984,Heath-Br.wnl2]showedthatforsufficientlylargex,#{nSx'd(n)=d(n 1)}>>x(logx)-'.(1.3)Inl987,Hi1debrand[31improvedthelowerboundto#{n5x:d(n)=d(n 1)}>>x(loglogx)-'.(1.4)Inthispaper5weprovethefollowingresult.Theorem.Smposek(22)isapositiveinteger.FOrsopcientlylarpex,#Ak(x):=#{nS…