所有双理想都是素双理想的半群

设S为一个半群,B是S的一个双理想(即B是S的一个满足条件BSBB的子半群)．如果对S的任意双理想C,D都有CDB蕴涵CB或DB,我们就称B为S的一个素双理想．如果K是一个N-覆盖的纯LR-带,我们就称K为一条拟链．本文证明了半群S的所有双理想都是素双理想的充分必要条件是S是一个幂等元形成拟链的纯整群并半群．     

非负矩阵的［0-单］单子半群

本文研究非负矩阵［0-单］单子半群,特别证明M_n(S)的［0-单］单子半群是完全［0-单］单的,其中S是强理想除0外每个元素都大于或等于1.最后举例说明非负矩阵 半群是一类有趣的半群.     

一类线性算子族在在t>0上的紧性

考虑了C1-正则半群{S(t)}t≥0和C2-正则半群{T(t)}t≥0之差Δ(t)=S(t)C1-T(t)C2在一定假定条件下的紧性.     

一类线性算子族在t〉0上的紧性

考虑了C1-正则半群{S（t）}t≥0和C2-正则半群{T（t）}t≥0之差△（t）=S（t）C1-T（t）C2在一定假定条件下的紧性．     

0-恰当半群

引入了0-恰当半群的概念,它是一种特殊的逆半群.给出了0-恰当半群的等价刻划.讨论具有幂等半格的右0-恰当半群上含于(够)0的最大同余关系μL和具有幂等半格的0-恰当半群上含于(形)0的最大同余关系μ.证明如果S是一个具有幂等半格E的右0-A型半群,则S/μL≌E当且仅当S是一个S0左逆的左消含幺半群的强半格.进一步证明了,如果S是一个具有幂等半格E的0-恰当半群,则S/μ≌E当且仅当S是一个S0逆的消去含幺半群的强半格.     

具有理想收缩性质的某些GV-半群(英文)

如果半群S的每一个理想都是它的幂等同态像,称半群S具有理想收缩性质。GV-半群是完全正则半群在π-正则半群范围内的推广。本文刻画了某些具有理想收缩性质的GV-半群。     

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.     

关于(A,B)型算子理想

对Gonz(?)lez和Martinon A新近建立的(A,B)型算子理想作进一步讨论,证明对任一算子理想B,(L,B)都是闭、满射的算子理想.证明对严格奇异算子理想S,(L,S)就是S的闭、满射包,也就是Rosenthal算子理想.     

半群的(∈,∈ ∨q(λ,μ))-模糊k-理想(英文)

本文研究了半群中的广义模糊k-理想和(∈,∈∨q(λ,μ))-模糊k-理想.利用模糊集的截集及模糊集的性质,获得了(∈,∈∨q(λ,μ))-模糊k-理想的等价刻画,广义模糊特征化及广义模糊k-理想直积的基本性质.最后还给出了半群S是左k-诺特的充要条件是对于S的任意广义模糊左k-理想A,Im(A)是[λ,μ]上的良序子集.这些结果有重要的理论价值.     

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.     

A Note on Polynomially Growing C<Subscript>0</Subscript>-Semigroups

We characterize polynomial growth of a C₀-semigroup in terms of the first power of the resolvent of its generator. We do this for a class of semigroups which includes C₀-semigroups on Hilbert spaces and analytic semigroups on Banach spaces. Furthermore, we characterize polynomial growth for discrete semigroups.     

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.     

Maximal semigroups dominated by 0–1 matrices

Maximal semigroups dominated by a 0–1 matrix of a certain type are determined. The 0–1 matrices that dominate maximal bounded and maximal commuting semigroups are given. Also semigroup modules over maximal semigroups dominated by a 0–1 matrix are discussed.     

c0空间上生灭矩阵生成半群的条件

本讨论了c0空间上生灭矩阵生成C0-半群的条件,并证明了该生成的半群是一正的压缩半群。     

C0-半群理论在动态M／C／1排队系统中的应用

考察了动态M／G／1排队系统问题．利用泛函分析中的C0-半群理论给出了系统非负解的存在唯一性．     

弱P—正则半群

在本文中,我们刻画弱P－正则半群上的最大幂等分离同余,并且证明了有超C－集的弱P－正则半群S[P]是拟P－正则当且仅当它同构于WB（p)[P^*]和某个弱正则^*-半群T的织积,其中B是S[P]的半带,最后,我们获得,在一般情况下,WB(p)[P]的弱P－正则半群但不是P－正则半群的条件。     

Lack of uniformly exponential stabilization for isometric -semigroups under compact perturbation of the generators in Banach spaces

This paper is concerned with non-uniformly exponential stabilization for infinite-dimensional linear systems under compact feedback in Banach spaces. We prove that a compact perturbation of the generator of an isometric -semigroup cannot generate a uniformly exponentially stable -semigroup in a Banach space. Finally, examples are provided to illustrate our result.

     

Completions for partially ordered semigroups

A standard completion γ assigns a closure system to each partially ordered set in such a way that the point closures are precisely the (order-theoretical) principal ideals. If S is a partially ordered semigroup such that all left and all right translations are γ-continuous (i.e., Y∈γS implies {x∈S:y·x∈Y}∈γS and {x∈S:x·y∈Y}∈γS for all y∈S), then S is called a γ-semigroup. If S is a γ-semigroup, then the completion γS is a complete residuated semigroup, and the canonical principal ideal embedding of S in γS is a semigroup homomorphism. We investigate the universal properties of γ-semigroup completions and find that under rather weak conditions on γ, the category of complete residuated semigroups is a reflective subcategory of the category of γ-semigroups. Our results apply, for example, to the Dedekind-MacNeille completion by cuts, but also to certain join-completions associated with so-called “subset systems”. Related facts are derived for conditional completions. A first draft of this paper by the second author, containing parts of Section 2, was received on August 9, 1985.