序半群中的粗糙理想

引入了序半群中(上,下)粗糙理想的概念,讨论了序半群中理想与(上,下)粗糙理想的关系,证明了对含最小元的序半群,若任一元素的等价类是有限的,则下粗糙理想之集关于包含序构成一个代数格。最后,讨论了(半,准)素理想与(上,下)粗糙(半,准)素理想的关系。     

序半群素模糊理想的刻画

研究序半群S的素模糊理想,通过S的模糊左（右）理想和序模糊点给出了S的素模糊理想的等价刻画。     

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．     

可除半环的伪理想与同余

引入可除半环的伪理想,它与同余互相唯一决定,在可除半环中利用理想作商是可行的,并证明了同态基本定理.     

格蕴涵N序半群中的sl理想

研究由格蕴涵代数所诱导的格蕴涵N序半群的sl理想的代数特性，给出了格蕴涵代数L中的LI-理想与相应的格蕴涵N序半群中的sl理想以及理想之间的关系定理，并对由集合A所生成的sl理想进行了刻画。最后，讨论了L中的准素sl理想和素sl理想之间的关系。     

关于poe—半群的双理想

推广正则半群中的双理想到ｐｏ－半群之中，利用ｐｏ－半群中的双理想研究了正则ｐｏｅ－半群、内正则ｐｏｅ－半群。得到了如下主要结果：①Ｓ为正则ｄｕｏ的充要条件是：Ｂ（ａｂ）＝Ｂ（ａ）∩Ｂ（ｂ），Ａ↓ａ、ｂ∈Ｓ；②Ｓ正则ｄｕｏ的充要条件为Ｓ为Ｂ－单序半群的半格；③Ｓ内正则的充要条件为：Ｒ∩Ｂ∩Ｌ包含于（ＬＢＲ］；④Ｓ正则且内正则的充要条件为：Ｒ∩Ｂ∩Ｌ包含于（ＢＲＬ］。     

半环上Fuzzy k-理想的再定义

本文中，给出Fuzzy k－理想的新的概念作为半环上k－理想的新的模糊化概念，研究了半环同态下的Fuzzy k－理想的象及逆象的有关性质，并给出了非负整数半环N的Fuzzy k－理想的构造。     

半环上的三角矩阵乘法半群的自同构

设R是含有恒等元1的半环,C是R上的中心子半环.Tn(R)是R上的n阶上三角矩阵C-代数.证明了当R是一个幂等元都是中心元的半环时,映射Φ:Tn(R)→Tn(R)是乘法半群自同构当且仅当存在Tn(R)中的可逆矩阵G和R中的半环自同构τ使得A=(aij)n×n∈Tn(R),均有Φ(A)=G-1τ(A)G.这里τ(A)=(τ(aij))n×n,n2.     

半环中带算子的L-模糊h-理想

The notions of M-hemirings and L-fuzzy left h-ideals with operators in M-hemirings are introduced,and some properties are investigated.Given an L-fuzzy left h-ideal with operators,a new L-fuzzy left h-ideal with operators is established. Using a collection of left M-h-ideals,L-fuzzy left h-ideais with operators are con- structed.Moreover,the concept of M-Notherian M-hemiring is introduced and its characterization is given.     

基于可减的实半环与实素理想

半环R被称为实半环,若对于任意的n∈N,方程x1^2＋…＋xn^2=0在R中只有零解：x1=…=xn=0.为了刻画实半环,引入了实理想和极小素理想的概念,利用同余的方法,得到了可减半环类中实半环的结构定理.     

Fuzzy Ideals and Fuzzy Interior Ideals in Ordered Semirings

The notions of fuzzy ideals and fuzzy interior ideals in ordered semirings are introduced and some of their characterizations are obtained through regularity criterion and with some operations on them.     

On L-fuzzy Ideals in Semirings I

In this paper we extend the concept of an L-fuzzy (characteristic) left (resp. right) ideal of a ring to a semiring R, and we show that each level left (resp. right) ideal of an .L-fuzzy left (resp. right) ideal of R is characteristic iff is L-fuzzy characteristic.     

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.     

半环上同余的刻画

引入半环的完全素理想的概念.利用这一概念,研究了半环的同余,分别给出了半环的子直积分解的若干结果和半环同余的一种刻画.     

On Ordered Semigroups Containing Covered Ideals

A proper ideal M of an ordered semigroup (S, ·, ≤) is said to be a covered ideal of S if M ? (S(S?M)S], i.e., if for any x in M, there exist a, c in S and b in S?M such that x ≤ abc. The purpose of this article is to study the structure of ordered semigroups containing covered ideals. The results obtained generalize the results on semigroups (without order) studied by Fabrici in 1984.     

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.     

双极值模糊集在半环上的应用

On the basis of concepts of bipolar fuzzy sets, we establish a new framework of bipolar fuzzy subsemirings（resp., ideals） which is a generalization of traditional fuzzy subsemirings（resp., ideals） in semirings. The concepts of bipolar fuzzy subsemirings（resp., ideals） are introduced and related properties are investigated by means of positive t-cut, negative s-cut and equivalence relation. Particularly, the notion of a normal bipolar fuzzy ideal is given, and some basic properties are studied in this paper.     

Regularity Criterion for Complete Matrix Semirings

Necessary and sufficient conditions for the regularity of complete matrix semirings over an arbitrary semiring are obtained.     

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．     

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