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1.
Characterization theorems for abundant sernigroups having a quasi-ideal quasi-adequate transversal are obtained. Our results generalize and amplify the related results of Satio on regular semigroup obtained in 1985 and Kong obtained in 2007 respectively. Some recent results on this topic given by Guo-Shum are strengthened. In particular, the structure of such an abundant semigroup is described. 相似文献
2.
The so-called split IC quasi-adequate semigroups are in the class of idempotent-connected quasi-adequate semigroups. It is
proved that an IC quasi-adequate semigroup is split if and only if it has an adequate transversal. The structure of such semigroup
whose band of idempotents is regular will be particularly investigated. Our obtained results enrich those results given by
McAlister and Blyth on split orthodox semigroups. 相似文献
3.
Xiangfei Ni 《代数通讯》2013,41(7):2433-2447
In this article, we explore the multiplicative quasi-adequate transversals of an abundant semigroup. Let S be an abundant semigroup with multiplicative quasi-adequate transversals. Then the product of any two multiplicative quasi-adequate transversals is also a multiplicative quasi-adequate transversal. Moreover, all multiplicative quasi-adequate transversals of S form a rectangular band. Let S°and S ? be multiplicative quasi-adequate transversals of S, and let δ°(δ?) be the δ-relation on S°(S ?). Then there exists a bijection ? from S°/δ°onto S ?/δ?. In particular, if δ°and δ? are congruences, then the bijection ? is an isomorphism. 相似文献
4.
Abundant semigroups with a multiplicative type A transversal 总被引:10,自引:0,他引:10
Abdulsalam El-Qallali 《Semigroup Forum》1993,47(1):327-340
5.
The notion of an inverse transversal of a regular semigroup is well-known. Here we investigate naturally ordered regular semigroups
that have an inverse transversal. Such semigroups are necessarily locally inverse and the inverse transversal is a quasi-ideal.
After considering various general properties that relate the imposed order to the natural order, we highlight the situation
in which the inverse transversal is a monoid. The regularity of Green’s relations is also characterised. Finally, we determine
the structure of a naturally ordered regular semigroup with an inverse monoid transversal. 相似文献
6.
Jehan Al-Bar 《代数通讯》2013,41(7):2309-2324
We consider adequate transversals of abundant semigroups and prove that, in a particular case, there is a natural embedding of an inverse transversal within a certain regular subsemigroup. We also introduce the concepts of simplistic, perfect, and quasi-adequate transversal and provide a number of interesting connections between these. 相似文献
7.
Abundant Semigroups with a Multiplicative Adequate Transversal 总被引:6,自引:0,他引:6
Xiao Jiang Guo 《数学学报(英文版)》2002,18(2):229-244
The aim of this paper is to investigate abundant semigroups with a multiplicative adequate transversal. Some properties and
characterizations for such semigroups are obtained. In particular, we establish the structure of this class of abundant semigroups
in terms of left normal bands, right normal bands and adequate semigroups with some simple compatibility conditions. Finally,
we apply this structure to some special cases.
Received February 25, 1999, Revised November 22, 1999, Accepted December 9, 1999 相似文献
8.
9.
本文首先研究了具有可消模断面的拟恰当半群的结构,然后给出了用可消模断面的拟恰当半群构造具有CO-恰当断面富足半群的方法. 相似文献
10.
In this paper, some properties of good homomorphic images of abundant semigroups with a multiplicative quasi-adequate transversal
are obtained. After that, good congruences on a class of abundant semigroups with such transversals are studied. We characterize
the good congruences by using the so-called good congruence triple. Furthermore, we prove that any good congruence on a class
of abundant semigroups with such transversals can be constructed by the good congruence triple. 相似文献
11.
The aim of this article is to study naturally ordered abundant semigroups in which every idempotent has a greatest inverse. After obtaining some characterizations, their structure is established. 相似文献
12.
本文引入并研究了左简纯正断面, 得到了与之相关的若干刻画; 推广并丰富了Blyth 和AlmeidaSantos 于1996 年得到的关于左简逆断面及Kong 于2007 年得到的关于纯正断面的相关结果; 同时,给出了具有左简纯正断面的正则半群的结构定理. 相似文献
13.
具有弱正规幂等元的富足半群的结构 总被引:7,自引:1,他引:6
本文研究含弱正规幂等元的富足半群.在给出这类半群的若干特征后,建立了具有弱正规幂等元的富足半群的结构.作为应用,给出具有正规幂等元的富足半群和具有(弱)正规幂等元的拟适当半群的结构. 相似文献
14.
Shoufeng Wang 《Periodica Mathematica Hungarica》2016,72(1):43-49
In this note, we consider the Erd?s–Straus Diophantine equation where n and c are positive integers with \(\gcd (n, c) = 1\). We provide a formula for the number f(n, c) of all positive integral solutions (x, y, z) of the equation. In 1948, Erd?s and Straus conjectured that \(f(n,4) \ge 1,\) for all integers \(n \ge 2\). Here, we solve the conjecture for a special case of n.
相似文献
$$\begin{aligned} \frac{c}{n}=\frac{1}{x} + \frac{1}{y} + \frac{1}{z}, \end{aligned}$$
15.
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. 相似文献
16.
给出了具有Clifford断面的右正规纯正半群的等价刻画,得到了具有Clifford断面的正则纯正半群的次直积分解,证明了具有Clifford断面的正则纯正半群一定是正则纯正群. 相似文献
17.
利用格林*-关系刻画R和L并给出与它们相关的一些性质.利用R和L,得到恰当断面是拟理想的几个等价条件.最后,用两个结构构件R和L给出具有拟理想恰当断面的富足半群的一个结构定理.它比陈建飞在2000年给出的要简单. 相似文献
18.
By an associate inverse subsemigroup of a regular semigroup S we mean a subsemigroup T of S containing a least associate of each x∈S, in relation to the natural partial order ≤
S
. We describe the structure of a regular semigroup with an associate inverse subsemigroup, satisfying two natural conditions.
As a particular application, we obtain the structure of regular semigroups with an associate subgroup with medial identity
element.
Research supported by the Portuguese Foundation for Science and Technology (FCT) through the research program POCTI. 相似文献
19.
Torben Maack Bisgaard 《Journal of Theoretical Probability》1996,9(3):631-645
If (
j
) is a sequence of measures onR
k
having momentss
n
(
j
) of all ordersnN
0
k
and if for eachnN
0
k
the sequence (s
n
j
))
jN
converges to somet
n
R then some subsequence of (
j
) converges weakly to a measure with moments of all orders satisfyings
n
()=t
n
for allnN0/k
. Thisindeterminate method of moments and the continuity theorems in probability theory suggest a common generalization, dealing with a commutative semigroupS, with involution and a neutral element, and measures on the dual semigroupS
* ofcharacters on S—hermitian multiplicative complex functions not identically zero. In this setting, a continuity theorem holds for measures on the set of bounded characters,(2) and an indeterminate method of moments whenS is finitely generated.(2) The latter result is generalized in the present paper to the case of arbitraryS. This leads to a generalization of Haviland's criterion for theK-moment problem, and to a continuity theorem for the so-called perfect semigroups. 相似文献
20.
本文主要研究了具有乘适当断面无交并性质的富足半群的若干性质,并证明了半群为具有乘适当断面无交并性质的富足半群当且仅当它是一个矩形带和适当半群的直积。 相似文献