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.     

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.     

Block-separating Congruence Lattices of E-bisimple Semigroups

In this paper,we study block-separating congruences on E-bisimple semigroups. We describe two congruence relations T and W on the lattice of block-separating congruences, where the latter is defined in this paper. We determine the greatest and smallest congruences in T-classes and W-classes.     

序半群的正则同余类

本文的目的是给出一个序半群的子集能成为某个正则同余的同余类的刻面,同时我们可以容易看出[5]中的关于一般半群(没有序关系)的相应的结论仅是本文的结论的应用.     

Semigroups with the Congruence Extension Property

ρT on a semigroup of T of S extends to the semigroup S, if there exists a congruence _ρ on s such that _{ρ|T= ρT}. A semigroup S has the congruence extension property, CEP, if each congruence on each semigroup extends to S. In this paper we characterize the semigroups with CEP by a set of conditions on their structure (by this we answer a problem put forward in [1]). In particular, every such semigroup is a semilattice of nil extensions of rectangular groups.     

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     

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     

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.     

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.     

Inverse Near Permutation Semigroups

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 G of permutations on N elements and by a set H of transformations of rank N - 1. In this paper we give necessary and sufficient conditions for a near permutation semigroup S = ‹G,H›, where H is a group, to be inverse. Moreover, we obtain conditions which guarantee that its semilattice of idempotents is generated by the idempotents of S of rank greater than N - 2 or N - 3.     

Block Separating Congruence Lattices of E－bisimple Semigroups

In 1966, Reilly Characterized bisimple ω-semigroups as Bruck-Reilly extensions of Groups.Later, Munn and Reilly proved that a congruence on a bisimple ω-semigroup is a group congruence or is idempotent-separating. Many author investigated the congruences on Bruck-Reilly ex-     

Unary Iterative Hyperidentities for Semigroups and Inverse Semigroups

Research supported by NSERC.     

含幺逆半群的半格上的同余格

本文证明了含幺逆半群Sα（α∈Y）的半格的容许同余格同构于半格S上同余格的一个子格。