序半群的滤子与Green关系

给出了半格同余N分别为Green关系L，R，Z和H之一的序半群的刻画。     

序半群的正则同余类

本文的目的是给出一个序半群的子集能成为某个正则同余的同余类的刻面,同时我们可以容易看出[5]中的关于一般半群(没有序关系)的相应的结论仅是本文的结论的应用.     

利用二阶上三角矩阵构造各类非交换的序群

利用二阶上三角矩阵分别构造了非交换的序群、拟序群、拟偏序群和拟格序群.     

Archimedean ordered semigroups as ideal extensions

The main result of the paper is a structure theorem concerning the ideal extensions of archimedean ordered semigroups. We prove that an archimedean ordered semigroup which contains an idempotent is an ideal extension of a simple ordered semigroup containing an idempotent by a nil ordered semigroup. Conversely, if an ordered semigroup S is an ideal extension of a simple ordered semigroup by a nil ordered semigroup, then S is archimedean. As a consequence, an ordered semigroup is archimedean and contains an idempotent if and only if it is an ideal extension of a simple ordered semigroup containing an idempotent by a nil ordered semigroup.     

偏序集上蕴涵代数的素滤子

偏序集上的蕴涵代数是取值于偏序集上的蕴涵逻辑联结词的一种代数抽象.以偏序集上蕴涵代数中由蕴涵算子引入的逻辑运算t-余范为工具,讨论了偏序集上蕴涵代数的一些性质,然后引入了偏序集上蕴涵代数的素滤子的概念,讨论了素滤子在一定条件下的性质,并给出了一个MP滤子成为素滤子的条件.     

On Pseudocomplemented and Stone Ordered Sets

The aim of this paper is to characterize both the pseudocomplemented and Stone ordered sets in a manner similar to that used previously for Boolean and distributive ordered sets. The sublattice G(A) of the Dedekind–Mac Neille completion DM(A) of an ordered set A generated by A is said to be the characteristic lattice of A. We will show that there are distributive pseudocomplemented ordered sets whose characteristic lattices are not pseudocomplemented. We can define a stronger notion of pseudocomplementedness by demanding that both A and G(A) be pseudocomplemented. It turns out that the two concepts are the same for finite and Stone ordered sets.     

Soft ordered semigroups

Molodtsov introduced 1999 the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to ordered semigroups. The notions of (trivial, whole) soft ordered semigroup, soft ordered subsemigroup, soft left (right) ideal, and left (right) idealistic soft ordered semigroup are introduced, and various related properties are investigated (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

序半群的一类正则同余

设S是有向序半群,本文给出了S上的一类正则同余,称为强序同余的定义及性质.证明了S的强序同余是强正则同余,但反之不成立.同时证明了强序同余格SOC(S)是S的同余格C(S)关于通常集合的交和传递积的V-完备的分配子格.     

PARTIALLY ORDERED CONNECTIVES

We show that a coherent theory of partially ordered connectives can be developed along the same line as partially ordered quantification. We estimate the expressive power of various partially ordered connectives and use methods like Ehrenfeucht games and infinitary logic to get various undefinability results.     

序半环的序理想

An ordered semiring is a semiring S equipped with a partial order ≤ such that the operations are monotonic and constant 0 is the least element of S.In this paper,several notions,for example,ordered ideal,minimal ideal,and maximal ideal of an ordered semiring,simple ordered semirings,etc.,are introduced.Some properties of them are given and characterizations for minimal ideals are established.Also,the matrix semiring over an ordered semiring is consid-ered.Partial results obtained in this paper are analogous to the corresponding ones on ordered semigroups,and on the matrix semiring over a semiring.     

关于序半群的模糊拟理想

In this paper,fuzzy quasi-ideals of ordered semigroups are characterized by the properties of their level subsets.Furthermore,we introduce the notion of completely semiprime fuzzy quasi-ideals of ordered semigroups and characterize strongly regular ordered semigroups in terms of completely semiprime fuzzy quasi-ideals.Finally,we investigate the characterizations and decompositions of left and right simple ordered semigroups by means of fuzzy quasi-ideals.     

A Characterization of 1-, 2-, 3-, 4-Homomorphisms of Ordered Sets

We characterize totally ordered sets within the class of all ordered sets containing at least four-element chains. We use a simple relationship between their isotone transformations and the so called 1-endomorphism which is introduced in the paper. Later we describe 1-, 2-, 3-, 4-homomorphisms of ordered sets in the language of super strong mappings.     

Transformational antiatomic characteristic of ordered sets

To any ordered set with a universally maximal element, a semigroup of its transformations with some natural properties that defines the ordered set up to an isomorphism is assigned. The system of such transformation semigroups is proved to be the minimal element in the set of all defining systems of transformation semigroups with respect to the following ordering: one system precedes another if for each ordered set from the class in question, the semigroup of its transformation belonging to the first system is contained in the semigroup of its transformation from the second system. Translated fromMatematicheskie Zametki, Vol. 66, No. 1, pp. 112–119, July, 1999.     

完备稠序线性序拓扑空间上的奇周期轨序关系

研究完备稠序线性序拓扑空间上连续自映射的周期轨,指出当连续自映射有（2n＋1）-周期轨而没有（2n-1）-周期轨时,该（2n＋1）-周期轨上各点的序关系.利用这个关系将Sharkovskii定理从实直线推广到完备稠序线性序拓扑空间上。     

Some Characterizations of Strongly Semisimple Ordered Semigroups

In this paper, the concept of quasi-prime fuzzy left ideals of an ordered semigroup $S$ is introduced. Some characterizations of strongly semisimple ordered semigroups are given by quasi-prime fuzzy left ideals of $S$. In particular, we prove that $S$ is strongly semisimple if and only if each fuzzy left ideal of $S$ is the intersection of all quasi-prime fuzzy left ideals of $S$ containing it.     

Totally ordered sets and the prime spectra of rings

Let T be a totally ordered set and let D(T) denotes the set of all cuts of T. We prove the existence of a discrete valuation domain O_v such that T is order isomorphic to two special subsets of Spec(O_v). We prove that if A is a ring (not necessarily commutative), whose prime spectrum is totally ordered and satisfies (K2), then there exists a totally ordered set U?Spec(A) such that the prime spectrum of A is order isomorphic to D(U). We also present equivalent conditions for a totally ordered set to be a Dedekind totally ordered set. At the end, we present an algebraic geometry point of view.     

全序幂等元剩余格

研究了全序幂等元剩余格,给出了全序幂等元剩余格的另一种新的构造方法,并且得到了这类剩余格的结构定理,推广了相关文献的结论．     

On congruences and ideals of partially ordered quasigroups

Some results concerning congruence relations on partially ordered quasigroups (especially, Riesz quasigroups) and ideals of partially ordered loops are presented. These results generalize the assertions which were proved by Fuchs in [5] for partially ordered groups and Riesz groups.     

Hierarchies of Partially Ordered Connectives and Quantifiers

Connections between partially ordered connectives and Henkin quantifiers are considered. It is proved that the logic with all partially ordered connectives and the logic with all Henkin quantifiers coincide. This implies that the hierarchy of partially ordered connectives is strongly hierarchical and gives several nondefinability results between some of them. It is also deduced that each Henkin quantifier can be defined by a quantifier of the form what is a strengthening of the Walkoe result. MSC: 03C80.     

弱可约序半群的理想扩张

NioviKehayopulu和Michael Tsingelis于2003年给出了关于序半群的理想扩张的一个定理,本文利用该定理进一步给出了弱可约序半群的理想扩张的构造．