具有Clifford断面的正则纯正半群

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．     

具有Clifford断面的纯正半群

本文研究有Clifford断面的纯正半群.为了获得主要的结构定理，证明了纯正半群有群断面当且仅当它是矩形群;利用半格和矩形带，建立了有Clifford断面的纯正半群的结构.     

Clifford流形

本文将Cauchy-Riemann方程推广到Clifford变量的Clifford值函数,并由此将复流形和殆复流形理论及四元数流形理论的某些结果推广到更一般的所谓Clifford流形.     

Expression for the Group Inverse of the 2 × 2 Blo ck Matrix

In this paper, we present a method how to get the expression for the group inverse of 2 × 2 block matrix and get the explicit expressions of the block matrix ?A C ? BD under some conditions.     

ON THE REVERSE ORDER LAW (AB)D=BDAD

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Unified Approach to the Expression for the Moore-Penrose Inverse of a- xy

Let .4 be an unital C＊-algebra, a,x and y are elements in .A. In this paper, we present a method how to calculate the Moore-Penrose inverse of a - xy＊ and investigate the expression for some new special cases of （a - xy）.     

E-自反逆半群上的Clifford同余

研究E-自反逆半群上的Clifford同余.本文中的结果是James[1],McAlister[2],Petrich[3]和Reilly[4]等人关于E-酉逆半群上的相应同余定理在E-自反逆半群上的自然推广.     

具有某种断面的半群的研究进展

本文综述了几类具有特殊断面的半群的近期研究结果。在介绍逆半群和正则半群的一般结构之后，概述了具有逆断面的正则半群的结构和同余格的研究成果。总结了作为逆断面的推广的可裂断面，纯正断面，正则^*－断面和恰当断面。提出了可以进一步研究的重要的问题。     

具有左单S-恰当断面的富足半群的结构(英文)

本文得到具有左单恰当断面的富足半群的进一步刻画.推广并丰富了Blyth和AlmeidaSantos于1996年得到的关于左单逆断面及两位作者分别于2008年与2010年得到的关于恰当断面的相关结果.建立了具有左单S-恰当断面的富足半群的结构.     

具有拟理想正则*-断面的正则半群

本文提出了具有正则*-断面正则半群的概念，所给出的例子表明具有拟理想正则*-断面的正则半群类真包含了具有拟理想逆断面的正则半群类和正则*-半群类；最后刻画了具有拟理想正则*-断面的正则半群的结构．     

具有左简纯正断面的正则半群

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.     

Regular semigroups with weakly simplistic orthodox transversals

Weakly simplistic orthodox transversals are introduced in this paper and some characterizations associated with them are obtained. An example is given to demonstrate that weakly simplistic orthodox transversals are proper generalisations of left simplistic orthodox transversals. The related results of Blyth and Almeida Santos on left simplistic inverse transversals obtained in 1996 and Kong and Luo on left simplistic orthodox transversals obtained in 2011 are generalised and amplified. A structure theorem of regular semigroups with weakly simplistic orthodox transversals is also established.     

HOPs and COPs: Room frames with partitionable transversals

In this paper, we construct Room frames with partitionable transversals. Direct and recursive constructions are used to find sets of disjoint complete ordered partitionable (COP) transversals and sets of disjoint holey ordered partitionable (HOP) transversals for Room frames. Our main results include upper and lower bounds on the number of disjoint COP transversals and the number of disjoint HOP transversals for Room frames of type 2ⁿ. This work is motivated by the large number of applications of these designs.     

On Generalized Orthodox Transversals

Generalized orthodox transversals are introduced in this article, and some characterizations associated with them are obtained. The related results of Chen on quasi-ideal orthodox transversals obtained in 1999 and Zhang and Wang on generalized inverse transversals obtained in 2008 are generalized and amplified. A structure theorem of a regular semigroup with a perfect generalized orthodox transversal is also established.     

The generalization of two basic results for orthodox semigroups

A characterization of orthodox transversals is given and the maximum idempotent-separating congruence concerned with quasi-ideal orthodox transversals is explored. The well-known results about orthodox semigroups are generalized and enriched.     

Free orthodox semigroups and free bands with inverse transversals

It is well known that the subclass of inverse semigroups and the subclass of completely regular semigroups of the class of regular semigroups form the so called e-varieties of semigroups. However, the class of regular semigroups with inverse transversals does not belong to this variety. We now call this class of semigroups the ist-variety of semigroups, and denote it by IST. In this paper, we consider the class of orthodox semigroups with inverse transversals, which is a special ist-variety and is denoted by OIST. Some previous results given by Tang and Wang on this topic are extended. In particular, the structure of free bands with inverse transversals is investigated. Results of McAlister, McFadden, Blyth and Saito on semigroups with inverse transversals are hence generalized and enriched.     

带有乘右适当断面的右主投射半群(英文)

In this paper,the concept of right adequate transversals of rpp semigroups is introduced.We establish the structure of rpp semigroups with multiplicative right adequate transversals in terms of right normal bands and right adequate semigroups.In particular, some special cases are considered.     

Quasi-ideal transversals of abundant semigroups and spined products

We provide a new and much simpler structure for quasi-ideal adequate transversals of abundant semigroups in terms of spined products, which is similar in nature to that given by Saito in Proc. 8th Symposium on Semigroups, pp. 22–25 (1985) for weakly multiplicative inverse transversals of regular semigroups. As a consequence we deduce a similar result for multiplicative transversals of abundant semigroups and also consider the case when the semigroups are in fact regular and provide some new structure theorems for inverse transversals.     

On the Multiplicative Quasi-Adequate Transversals of an Abundant Semigroup

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.     

Parallel focal structure and singular Riemannian foliations

We give a necessary and sufficient condition for a submanifold with parallel focal structure to give rise to a global foliation of the ambient space by parallel and focal manifolds. We show that this is a singular Riemannian foliation with complete orthogonal transversals. For this object we construct an action on the transversals that generalizes the Weyl group action for polar actions.