Regularity on Near Permutation Semigroups

Abstract

A transformation semigroup over a set X with N elements is said to be a near permutation semigroup if it is generated by a group of permutations on N elements and by a set of transformations of rank N ? 1. The aim of this paper is to determine computationally efficient conditions to test whether or not a near permutation semigroup is regular.     

Inverse wpp Semigroups

It is dedicated to the study of inverse wrpp semigroup, we obtain some charac- terizations of inverse wpp semigroup. In particular, we establish some charactizations for C-wrpp semigroup.     

Zero-Semidistributive Inverse Semigroups

An inverse semigroup S is said to be 0-semidistributive if its lattice ?F (S) of full inverse subsemigroups is 0-semidistributive. We show that it is sufficient to study simple inverse semigroups which are not groups. Our main theorem states that such a simple inverse semigroup S is 0-semidistributive if and only if (1) S is E-unitary, (2) S is aperiodic, (3) for any a,b ∈ S/σ with ab ≠ 1, there exist nonzero integers n and m such that (ab) ^m  = a ⁿ or (ab) ^m  = b ⁿ , where σ is the minimum group congruence on S.     

具有逆断面的局部逆半群

Let S be a locally inverse semigroup with an inverse transversal S°. In this paper, we construct an amenable partial order on S by an R-cone. Conversely, every amenable partial order on S can be constructed in this way. We give some properties of a locally inverse semigroup with a Clifford transversal. In particular, if S is a locally inverse semigroup with a Clifford transversal, then there is an order-preserving bijection from the set of all amenable partial orders on S to the set of all R-cones of S.     

On Finite Semigroups Embeddable in Inverse Semigroups

No Abstract. October 29, 1998     

矩阵逆半群

讨论矩阵逆半群的一些基本性质, 证明矩阵逆半群的幂等元集是有限布尔格的子半格, 从而证明等秩矩阵逆半群是群, 然后完全确定二级矩阵逆半群的结构：一个二级矩阵逆半群或者同构于二级线性群,或者同构于二级线性群添加一个零元素,或者是交换线性群的有限半格, 或者满足其他一些性质; 对于由某些二级矩阵构成的集合, 我们给出了它们成为矩阵逆半群的充分必要条件.     

Normally Ordered Inverse Semigroups

NO of all normally ordered inverse semigroups. We show that the pseudovariety of inverse semigroups PCS generated by all semigroups of injective and order partial transformations on a finite chain consists of all aperiodic elements of NO . Also, we prove that NO is the join pseudovariety of inverse semigroups. PCS V G , where G is the pseudovariety of all finite groups.     

On Free Inverse Semigroups

Using techniques of Rewriting Theory, we present a new proof of the known theorem of Munn that FIX , the free inverse semigroup on X, is isomorphic to birooted word-trees on X.     

0-Semidistributive Inverse Semigroups

For an inverse semigroup S,the set L(S)of all inverse subsemigroups(including the empty set)of S forms a lattice with respect to intersection denoted as usual by ∩ and union,where the union is the inverse subsemingroup generated by inverse subsemigroups A,B of S.The set     

Compact Topological Inverse Semigroups

A locally compact commutative band with open principal ideals is a zero-dimensional scattered space. Cardinal invariants of locally compact and compact commutative bands with open principal ideals is investigated. A base of the topology of a compact commutative band with open principal ideals is determined and the structure of such compact semilattices in which every principal lower set is a chain is described. Every first countable compact inverse semigroup with open right (left, two-sided) principal ideals is metrizable     

Unary Iterative Hyperidentities for Semigroups and Inverse Semigroups

Research supported by NSERC.     

Regular Semigroups with Inverse Transversals

Let C be a semiband with an inverse transversal . In [7], G.T. Song and F.L. Zhu construct a fundamental regular semigroup with an inverse transversal . is isomorphic to a subsemigroup of the Hall semigroup of C but it is easier to handle. Its elements are partial transformations, and the operation-although not the usual composition-is defined by means of composition. Any full regular subsemigroup T of is a fundamental regular semigroup with inverse transversal . Moreover, any regular semigroup S with an inverse transversal is proved to be an idempotent-separating coextension of a full regular subsemigroup T of some . By means of a full regular subsemigroup T of some and by means of an inverse semigroup K satisfying some conditions, in this paper, we construct a regular semigroup with inverse transversal such that is isomorphic to K and to T. Furthermore, it is proved that if S is a regular semigroup with an inverse transversal then S can be constructed from the corresponding T and from in this way.     

完全单半群及完全正则半群的逆断面

指出完全单半群Ｓ的任何一个Ｆ－类是逆断面,且为Ｑ－逆断面,而Ｓ的任何一个逆断面必是一个Ｆ－类,因而所有逆断面同构。并且给出完全正则半群的逆断面存在的充要条件。     

Fundamental Regular Semigroups with Inverse Transversals

Abstract. Let C be a regular semigroup with an inverse transversal C° and let C be generated by its idempotents. Following W. D. Munn and T. E. Hall's idea, in this paper, a fundamental regular semigroup T _C,C° with an inverse transversal T _C,C° ° is constructed such that the following holds. For any regular semigroup S with an inverse transversal S° and < E(S)>=C , C°=C∩ S° , there is a homomorphism φ from S to T _C,C° such that the kernel of φ is the maximum idempotent-separating congruence on S , and φ satisfies: (1) φ| _C is a homomorphism from C onto < E(T _C,C° )> ; (2) φ| _S° is a homomorphism from S° to T _C,C° ° . In particular, S is fundamental if and only if S is isomorphic to a full subsemigroup of T _C,C° . Our fundamental regular semigroup T _C,C° is isomorphic to a subsemigroup of the Hall semigroup of C but it is easier to handle. Its elements are partial transformations, and the operation—although not the usual composition—is defined by means of composition.