Some properties of complete congruence lattices

For a complete lattice C, we consider the problem of establishing when the complete lattice of complete congruence relations on C is a complete sublattice of the complete lattices of join- or meet-complete congruence relations on C. We first argue that this problem is not trivial, and then we show that it admits an affirmative answer whenever C is continuous for the join case and, dually, co-continuous for the meet case. As a consequence, we prove that if C is continuous then each principal filter generated by a continuous complete congruence on C is pseudocomplemented. Received January 6, 1998; accepted in final form July 2, 1998.     

On a difference equation of the second order with an exponential coefficient

This paper is devoted to a generalization of some previous results, as we completely solve a linear homogeneous difference equation of the second order with an exponential coefficient.     

Congruence triples on regular semigroups and their generalizations

In this paper, we introduce the concept of VT-congruence triples on a regular semigroup S and show how such triples can be constructed by using the equivalences on S/ℒ, S/R and the special congruences on S. Also, such congruence triples are characterized so that an associated congruence can be uniquely determined by a given congruence triple. Moreover, we also consider the VH-congruence pairs on an orthocryptogroup.     

纯正半群上的强同余及其格

给出了纯正半群S的强同余格上同余T的一些判别性质,证明了S上所有基础强同余所构成的集合FCP（S）是CP（S）的完备子格,最后讨论了由纯正半群的正规子半群决定的交完备子格的结构及由“求核”运算确定的（交完备格）同余K的若干性质,还顺带讨论了群同余格.     

N(2,2,0)代数的稳定化子与同余分解

为了深入研究N(2,2,0)代数的代数结构,首先利用代数的推理方法进一步研究了N(2,2,0)代数的稳定化子,改进了以前学者的部分结果,然后利用稳定化子建立了一种同余关系,给出了N(2,2,0)代数的同余分解,证明了其商代数仍是N(2,2,0)代数,并获得了自然同态下一类逆像的代数结构和性质.     

半正定复方阵的Kronecker乘积

本文应用半正定（未必是Ｈｅｒｍｉｔｅ）复方阵在合同下的标准形给出两个半正定（未必是Ｈｅｒｍｉｔｅ）复方阵的Ｋｒｏｎｅｃｋｅｒ乘积为半正定的充要条件     

关于三维Minkowski空间中直线汇的一点补充

本文在[1]的基础上继续研究了三维Minkowski空间E31中,直线汇异于欧式空间的一些性质.     

分配半环上的可除半环同余

§ 1.　Introduction　　AsemiringSisanalgebraicsystem (S ,+ ,·)consistingofanon_emptysetStogetherwithtwobinaryoperations +and·onSsuchthat (S ,+ )and (S ,·)aresemigrolupscon nectedbyring_likedistributivity .AsemiringSiscalleddistributiveifinStheadditionisdis tributiveaboutmultiplication ,i.e .ab+c=(a+c) (b +c)anda+bc=(a +b) (a+c)holdforalla ,b ,c∈S .AsemiringSiscalleddivisibleif(S ,·)isagroup .AnequivalencerelationρonasemiringSiscalledacongruenceonS ,iffρisacongruenceon (S ,+ )and (…     

On Left Regular Ordered Semigroups

The main result of the paper is a decomposition theorem of the left regular ordered semigroups into left regular and left simple semigroups.     

Fuzzy同余和正规Fuzzy子群(英文)

自从A. Rosenfeld在1971年提出Fuzzy子群的概念以来,在Fuzzy群的研究方面已有不少进展,例如见[1,2,5,6,10,11,14]。另一方面,L.A.Zadeh首创的Fuzzy关系理论的研究也是硕果累累,例如见[3,4,8,12,13,15]。本文通过Fuzzy同余关系和正规Fuzzy子群的相互联系,将这两个方向的研究成果进行“嫁接”和“杂交”,得到许多有趣的结果。主要结果是定理2.7,定理3.1和3.6。本文另一主题是引入T-Fuzzy群的正规T-Fuzzy子群的新概念,当T是正则t-范算子时,得到了T-Fuzzy群的三个同构定理,作者认为它比现有的相应同构定理更为简洁、广泛和自然。