半群的模糊理想和模糊同余

引入半群上模糊理想、模糊同余的概念。给出它们的一些等价刻划,证明了一个半群上所有模糊同余关系作成一个格。最后,给出模糊理想的积和模糊同余关系的积的概念,讨论了它们的一些性质。     

伪补分配格的同余理想与同余关系

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。     

A note on CIP varieties

It is proved that every variety satisfying the Congruence Intersection Property (CIP) is Abelian. In addition, a CM Abelian variety has the CIP if and only if it has a constant term operation. Finally, a CM variety is Abelian if and only if it has the weak CIP. Received October 8, 1998; accepted in final form January 5, 1999.     

Classification of torsion-free genus zero congruence groups

We study and classify all torsion-free genus zero congruence subgroups of the modular group.

     

Generating primitive positive clones

Suppose is a set of operations on a finite set A. Define PPC() to be the smallest primitive positive clone on A containing . For any finite algebra A, let PPC#(A) be the smallest number n for which PPC(CloA) = PPC(Clo _n A). S. Burris and R. Willard [2] conjectured that PPC#(A) ≤|A| when CloA is a primitive positive clone and |A| > 2. In this paper, we look at how large PPC#(A) can be when special conditions are placed on the finite algebra A. We show that PPC#(A) ≤|A| holds when the variety generated by A is congruence distributive, Abelian, or decidable. We also show that PPC#(A) ≤|A| + 2 if A generates a congruence permutable variety and every subalgebra of A is the product of a congruence neutral algebra and an Abelian algebra. Furthermore, we give an example in which PPC#(A) ≥|A| - 1)² so that these results are not vacuous. Received August 30, 1999; accepted in final form April 4, 2000.     

分配伪补格的主理想

本文给出了分配伪补格 ( L;∧ ,∨ ,* ,0 ,1 )中的主理想 I=( d]成为同余理想的充分必要条件 .当 L是局部有限时 (即 d∈ S( L) ,Fd={x|x* * =d}有限 ) ,对骨架 S( L)中的每个元素 d,我们找到了以 I=( d]为核心的最小同余关系 ,利用以上结果我们得到一个 Stone代数是布尔代数的一些等价条件 .     

一类循环系的平坦性

设Ｓ是幺半群,ｘ_１,ｘ₂,…∈Ｓ且满足ｘ_i+１ｘ_i＝ｘ_i,ｉ＝１,２……ｙ是S中的任意元素,记H={(yx_i,x_i)|i=1,2,…}.设ρ(H)是S的由Ｈ生成的最小右同余,本文证明了S／ρ（Ｈ）是平坦右Ｓ－系．     

Special Elements of the Lattice of Overcommutative Varieties of Semigroups

The distributive, codistributive, standard, costandard, and neutral elements of the lattice of overcommutative varieties of semigroups are completely described.     

半群的模糊同余扩张

本文引入半群的模糊同余扩张的概念,给出了模糊同余扩张的同态性质,同时,本文研究了带有模糊同余扩张性质的半群类,证明了一个半群S有模糊同余扩张性质当且仅当S有同余扩张性质,最后进一步给出 有模糊同余张张性质的半群类的特征。     

同余式2n-2≡1（mod n）的一些新解

1991年,Sinisalo求出了同余式2n-2≡1（mod n）在区间[3,1011]上的所有解,共有88个,其中满足n≡9（mod 10）的解有6个.本文证明了,当n〈3.462＊1014时,同余式2n-2≡1（mod n）不存在有平方因子的解.利用一种新方法,借助计算机的Maple软件,得到了该同余式的9个含有平方因子的解.利用该方法,也可得到该同余式的许多大于1011的新解.