半群的(∈,∈∨q(λ,μ))-模糊n伪理想与Drazin半群的刻画

给出半群的模糊n伪理想,广义模糊n伪理想,(∈,∈∨q(λ,μ))-模糊n伪理想的定义,同时讨论了(∈,∈∨q(λ,μ))-模糊n伪左理想(右理想,理想)和广义模糊n伪左理想(右理想,理想)的等价刻画.还利用半群的广义模糊子系统来刻画Drazin半群的结构.     

半群的完全素和素模糊理想

通过由模糊点生成的模糊理想给出了半单半群的刻画。同时也刻画了两类半群：一类是所有模糊理想是素理想。另一类是所有模糊理想为安全素理想。     

On fuzzy ideals and fuzzy bi-ideals in semigroups

In this paper we give some properties of fuzzy ideals and fuzzy bi-ideals of semigroups, and characterize semigroups that are (left) duo, (left) simple and semilattices of subsemigroups in terms of fuzzy ideals and fuzzy bi-ideals.     

关于Fuzzy完全正则半群

本文先引入Ｆｕｚｚｙ左（Ｆｕｚｚｙ右）正则半群的概念，进而讨论Ｆｕｚｚｙ左（Ｆｕｚｚｙ右）正则半群以及Ｆｕｚｚｙ完全正则半群中Ｆｕｚｚｙ理想的一些代数性质。     

Fuzzy半群中的极小Fuzzy理想

本文先给出Ｆｕｚｙ半群中极小Ｆｕｚｙ理想的一些代数性质,进而利用极小Ｆｕｚｙ理想刻划Ｆｕｚｚｙ单半群的一些代数性质     

Fuzzy半群中的Fuzzy素理想

探讨Fuzzy半群中Fuzzy素理想,Fuzzy 完全理想与Fuzzy理想的根的一些代数性质,证明Fuzzy半群中每一个Fuzzy理想是Fuzzy完全半素理想当且仅当它可表为一族Fuzzy完全素理想之交。     

Some Characterizations of Left Weakly Regular Ordered Semigroups

In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and (generalized) bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.     

半群的模糊内理想

Abstract The concept of quasi-coincidence of a fuzzy interval value in an interval valued fuzzy set is a generalization of the quasi-coincidence of a fuzzy point in a fuzzy set. With this new concept, the interval valued （∈, ∈ Vq）-fuzzy interior ideal in semigroups is introduced. In fact, this kind of new fuzzy interior ideals is a generalization of fuzzy interior ideals in semigroups. In this paper, this kind of fuzzy interior ideals and related properties will be investigated. Moreover, the concept of a fuzzy subgroup with threshold is extended to the concept of an interval valued fuzzy interior ideal with threshold in semigroups.     

半群的模糊理论研究进展

介绍半群的模糊理论研究的基本内容、方法,重点介绍半群的模糊理想、模糊同余以及目前半群的模糊理论研究进展。     

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.     

Intuitionistic fuzzy semiprime ideals in ordered semigroups

We give characterizations of different classes of ordered semigroups by using intuitionistic fuzzy ideals. We prove that an ordered semigroup is regular if and only if every intuitionistic fuzzy left (respectively, right) ideal of S is idempotent. We also prove that an ordered semigroup S is intraregular if and only if every intuitionistic fuzzy two-sided ideal of S is idempotent. We give further characterizations of regular and intra-regular ordered semigroups in terms of intuitionistic fuzzy left (respectively, right) ideals. In conclusion of this paper we prove that an ordered semigroup S is left weakly regular if and only if every intuitionistic fuzzy left ideal of S is idempotent.     

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.     

Fuzzy Order Filters in Adjoint Semigroups of BCK-Algebras

In this paper, we introduce the notion of fuzzy order filters in adjoint semigroups of BCK-algebras. We prove that there is a bijection between the fuzzy ideals of BCK-algebras X and the fuzzy order filters in the adjoint semigroup M(X) of X.AMS Subject Classification (2000) 06F35 03G25 20M10     

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.     

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).     

Levi-Civita functional equations and the status of spectral synthesis on semigroups

We show, contrary to some published statements, that spectral synthesis does not generally hold for commutative semigroups that are not groups. On the positive side we prove that it holds if the semigroup is a monoid with no prime ideal. For semigroups with a prime ideal, the picture is not so clear. On the negative side we provide a variety of examples illustrating the failure of spectral synthesis for many semigroups with prime ideals, but we also give examples of semigroups with prime ideals on which spectral synthesis holds.

     

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.     

偏序半群的C-左理想

本文引入了偏序半群中Ｃ 左理想的概念，讨论了Ｃ 左理想的一些基本性质，定义了左基的概念并利用它给出了最大Ｃ 左理想存在的必要和充分条件．作为应用，本文还讨论了每个真左理想均为Ｃ 左理想和无Ｃ 左理想这两类半群的结构特征．本文的结果在一般半群中也成立     

Idempotent bounded C-semigroups

A semigroup with zero isidempotent bounded (IB) if it is the 0-direct union of idempotent generated principal left ideals and the 0-direct union of idempotent generated principal right ideals. Notable examples are completely 0-simple semigroups and the wider class of primitive abundant semigroups. Significant to the structure of these semigroups is that they are all categorical at zero. In this paper we describe IB semigroups that are categorical at zero in terms ofdouble blocked Rees matrix semigroups. This generalises Fountain's characterisation of primitive abundant semigroups via blocked Rees matrix semigroups [1], which in turn yields the Rees theorem for completely 0-simple semigroups.     

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).