关于序半群理想的根

Let S be an ordered semigroup.In this paper,we characterize ordered semigroups in which the radical of every ideal（right ideal,bi-ideal） is an ordered subsemigroup（resp.,ideal,right ideal,left ideal,bi-ideal,interior ideal） by using some binary relations on S.     

On ordered filters of implicative semigroups

In this paper, we first study how to generate an ordered filter by a set. Secondly, we discuss prime ordered filters in commutative implicative semigroups, and establish prime and irreducible decompositions Supported by the Basic Science Research Institute Program, Ministry of Education, 1994, Project No. BSRI-94-1406.     

阿基米德序半群的链(英文)

本文通过一个序半群S上的一些二元关系以及它的理想(右理想,双理想)的根集分别给出了该序半群是阿基米德(右阿基米德,t-阿基米德)序子半群的链的刻画.进一步证明了准素序半群是阿基米德序半群的链.最后,通过素根定理证明了序半群S是阿基米德序子半群的链当且仅当S是阿基米德序子半群的半格且S的所有素理想关于集合的包含关系构成链.     

On Ordered Semigroups Which are Semilattices of Simple and Regular Semigroups

We characterize the ordered semigroups which are decomposable into simple and regular components. We prove that each ordered semigroup which is both regular and intra-regular is decomposable into simple and regular semigroups, and the converse statement also holds. We also prove that an ordered semigroup S is both regular and intra-regular if and only if every bi-ideal of S is an intra-regular (resp. semisimple) subsemigroup of S. An ordered semigroup S is both regular and intra-regular if and only if the left (resp. right) ideals of S are right (resp. left) quasi-regular subsemigroups of S. We characterize the chains of simple and regular semigroups, and we prove that S is a complete semilattice of simple and regular semigroups if and only if S is a semilattice of simple and regular semigroups. While a semigroup which is both π-regular and intra-regular is a semilattice of simple and regular semigroups, this does not hold in ordered semigroups, in general.     

阿基米德序半群的链的若干刻画

本文首先引入了一个序半群$S$的准素模糊理想的概念,通过序半群$S$上的一些二元关系以及它的理想的模糊根给出了该序半群是阿基米德序子半群的半格的一些刻画.进一步地借助于序半群$S$的模糊子集对该序半群是阿基米德序子半群的半格进行了刻画.尤其是通过序半群的模糊素根定理证明了序半群$S$是阿基米德序子半群的链当且仅当$S$是阿基米德序子半群的半格且$S$的所有弱完全素模糊理想关于模糊集的包含关系构成链.     

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.     

Ordered semigroups whose elements are separated by prime ideals

In this paper we add one more characterization of intra-regular ordered semigroups in the existing bibliography by proving that the ordered semigroups whose elements are separated by prime ideals are actually the intra-regular ordered semigroups, a result which generalizes the corresponding result of semigroups (without order).     

Compact operator semigroups applied to dynamical systems

A right chain ordered semigroup is an ordered semigroup whose right ideals form a chain. In this paper we study the ideal theory of right chain ordered semigroups in terms of prime ideals, completely prime ideals and prime segments, extending to these semigroups results on right chain semigroups proved in Ferrero et al. (J Algebra 292:574–584, 2005).     

关于强可逆半准素序半群

把由G．Thierrin和A．Spoletini-Cherubini等人定义并研究的强可逆半群以及由S．Bogdanovic研究的半准素半群分别推广为强可逆序半群和半准素序半群．分别给出了半准素序半群和强可逆序半群类中的半准素序半群的刻划，还给出了其所有理想是素理想的强可逆序半群的刻划．     

关于交换序半群的一个注记

给出了正则交换序半群的与素理想结构有关的若干性质，还给出了为有限个主理想的并的交换序半群类中的诺特性，阿基米德性，正则性以及有限生成性之间的一些关系。     

CS-indecomposable ordered semigroups

An ordered semigroup S is called CS-indecomposable if the set S × S is the only complete semilattice congruence on S. In the present paper we prove that each ordered semigroup is, uniquely, a complete semilattice of CS-indecomposable semigroups, which means that it can be decomposed into CS-indecomposable components in a unique way. Furthermore, the CS-indecomposable ordered semigroups are exactly the ordered semigroups that do not contain proper filters. Bibliography: 6 titles. Published in Zapiski Nauchnykh Seminarov POMI, Vol. 343, 2007, pp. 222–232.     

序半群的阿基米德半群的半格分解

本文通过一个序半群S上的一些二元关系以及它的理想的根集的性质该序半群是阿基米德半群的半格,特别地是阿基米德半群的链的刻划,证明了S是阿基米德链当且仅当S是准素的.通过序半群的m-系的概念,证明了S的任意半素理想是含它的所有素理想的交,并通过该结论,证明了S是阿基米德半群的链当且仅当S是阿基米德半群的半格且S的所有素理想关于集包含关系构成链.作为应用,该结论在一般的半群（没有序）[1]中也成立.     

单的非负有序关联半群

一个负有序关联半群(S,≤,.,*)称为单的关联半群,如果S的所有滤子是{1}和S本身.对负有序关联半群是单的关联半群进行了刻画,给出了一个负的关联半群是单的关联半群的等价条件.     

Fuzzy Good Congruences on Left Semiperfect Abundant Semigroups

Motivated by studying fuzzy congruences in groups, semigroups, and ordered semigroups, and as a continuation of N. Kuroki and Y. Tan's works in regular semigroups in terms of fuzzy subsets, in this article we introduce the notions of a fuzzy good congruence relation, a fuzzy cancellative congruence relation on abundant semigroups, and give some properties, and characterizations of fuzzy good congruences on such semigroups. Furthermore, we characterize fuzzy good congruences of left semiperfect abundant semigroups, and get sufficient and necessary conditions for an abundant semigroup to be left semiperfect.     

On Priestley Spaces of Lattice-Ordered Algebraic Structures

The laws defining many important varieties of lattice-ordered algebras, such as linear Heyting algebras, MV-algebras and l-groups, can be cast in a form which allows dual representations to be derived in a very direct, and semi-automatic, way. This is achieved by developing a new duality theory for implicative lattices, which encompass all the varieries above. The approach focuses on distinguished subsets of the prime lattice filters of an implicative lattice, ordered as usual by inclusion. A decomposition theorem is proved, and the extent to which the order on the prime lattice filters determines the implicative structure is thereby revealed.     

Quantale中的素根定理

在Quantale中引入了m系的概念,利用m系讨论了Quantale中素理想和半素理想之间的关系.在此基础上证明了当Q是可换Quantale时,Id(Q)是空间式Quantale当且仅当Q中的任一理想都是半素理想.最后把环和序半群中的素根定理推广到Quantak中,得到了Quantale中的素根定理.     

QUOTIENT PRINCIPAL FACTORS OF AN ORDERED SEMIGROUP

In this paper, we introduce the concepts of 0-minimal ideals, 0-simple ordered semigroups, Rees factor ordered semigroups, natural QO-homomorphisms, quotient principal factors and semisimple ordered semigroups, and discuss characterizations, properties and relationships concerning them. Moreover, we generalize the principal series theory and relative ideal series theory of semigroups (without order) to general ordered semigroups and semisimple ordered semigroups, respectively.     

On (∈, ∈ ∨q k )-fuzzy ideals of ordered semigroups

In this paper, the concept of (∈, ∈ ∨q _k )-fuzzy ideals of an ordered semigroup S is introduced by the ordered fuzzy points of S, and related properties are investigated. Furthermore, we introduce the concept of prime (∈, ∈ q _k )-fuzzy ideals of ordered semigroups, and give some characterizations of them. As an application results of this paper, the corresponding results in ordinary semigroups can be also obtained by moderate modification.     

On quasi-prime,weakly quasi-prime left ideals in ordered-Γ-semigroups

In this paper we obtain and establish some important results in ordered Γ-semigroups extending and generalizing those for semigroups given in [PETRICH, M.: Introduction to Semigroups, Merill, Columbus, 1973] and for ordered semigroups from [KEHAYOPULU, N.: On weakly prime ideals of ordered semigroups, Math. Japon. 35 (1990), 1051–1056], [KEHAYOPULU, N.: On prime, weakly prime ideals in ordered semigroups, Semigroup Forum 44 (1992), 341–346] and [XIE, X. Y.—WU, M. F.: On quasi-prime, weakly quasi-prime left ideals in ordered semigroups, PU.M.A. 6 (1995), 105–120]. We introduce and give some characterizations about the quasi-prime and weakly quasi-prime left ideals of ordered-Γ-semigroups. We also introduce the concept of weakly m-systems in ordered Γ-semigroups and give some characterizations of the quasi-prime and weakly quasi-prime left ideals by weakly m-systems.     

自然序Dubreil-Jacotin富足半群

本文考虑Ｄｕｂｒｅｉｌ－Ｊａｃｏｔｉｎ富足半群,给出若干特征后,建立了自然序Ｄｕｂｒｅｉｌ－Ｊａｃｏｔｉｎ富足半群的结构,作为应用,给出了具有正则性条件的自然序Ｄｕｂｒｅｉｋｌ－Ｊａｃｏｔｉｎ富足半群的结构,并将结果推广到具有最大幂等元的自然序的偏序富足半群上。