Embedding theorems for proper inverse semigroups

  title={Embedding theorems for proper inverse semigroups},
  author={Liam O'Carroll},
  journal={Journal of Algebra},
  • L. O'Carroll
  • Published 1 September 1976
  • Mathematics
  • Journal of Algebra

Inverse Semigroups and Extensions of Groups by Semilattices

This paper is the first part of a series of three papers devoted to the study of inverse semigroups. The subject of our second paper [7] is free inverse semigroups, the third one [S] is dedicated to

The structure of pseudo-inverse semigroups

A regular semigroup S is called a pseudo-inverse semigroup if eSe is an inverse semigroup for each e= e2 C S. We show that every pseudo-inverse semigroup divides a semidirect product of a completely

Proper Weakly Left AMPLE Semigroups

It is shown how the structure of semigroups in this class is based on constructing semig groups from unipotent monoids and semilattices, a class with properties echoing those of inverse semiggroups.

Some covering and embedding theorems for inverse semigroups

Abstract An inverse semigroup S is called E-unitary if the equations ea = e = e2 together imply a2 = a. In a previous paper the author showed that every inverse semigroup is an idempotent separating

Inverse semigroups as extensions of semilattices

Let S be an inverse semigroup with semilattice of idempotents E, and let ρ be a congruence on S. Then ρ is said to be idempotent-determined [2], or I.D. for short, if (a, b) ∈ р and a∈E imply that b

Proper left type-A monoids revisited

The relation ℛ* is defined on a semigroup S by the rule that ℛ*b if and only if the elements a, b of S are related by the Green's relation ℛ in some oversemigroup of S. A semigroup S is an

Inverse semigroups with zero: covers and their structure

Abstract We obtain analogues, in the setting of semigroups with zero, of McAlister's convering theoren and the structure theorems of McAlister, O'Carroll, and Margolis and Pin. The covers come from a

Hnn Extensions of Semilattices

An HNN extension of a semilattice is shown to be a universal object in a certain category and an F-inverse cover over a free group for every inverse semigroup in the category.

A description of E-unitary inverse semigroups

  • Ross Wilkinson
  • Mathematics
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 1983
Synopsis An E-unitary inverse semigroup, S, has the property that, if x=S, and e2 = e=S, then (xe)2 = xe implies that x2 = x. As a consequence of this, we can see that S is an extension of its

Proper extensions of weakly left ample semigroups

SummaryWe consider proper (idempotent pure) extensions of weakly left ample semigroups. These are extensions that are injective in each <InlineEquation ID=IE"1"><EquationSource



Proper ordered inverse semigroups.

Let E be the subsemigroup of S constituted by all the idempotents of S. By a result of Munn, Γ = S/σ is an ordered group, where σ is the congruence relation such that xσy if and only if ex = ey for

Bisimple inverse semi-groups

In [1] Clifford showed that the structure of any bisimple inverse semigroup with identity is uniquely determined by that of its right unit subsemigroup. The object of this paper is to show that the

Bisimple Inverse Semigroups as Semigroups of Ordered Triples

In (8) and (13) it has been shown that certain bisimple inverse semigroups, called bisimple ω-semigroups and bisimple Z-semigroups, can be represented as semigroups of ordered triples. In these

A note on free inverse semigroups

  • L. O'Carroll
  • Mathematics
    Proceedings of the Edinburgh Mathematical Society
  • 1974
Recently Scheiblich (7) and Munn (3), amongst others, have given explicit constructions for FIA, the free inverse semigroup on a non-empty set A. Further, Reilly (5) has investigated the free inverse

The algebraic theory of semigroups

This book, along with volume I, which appeared previously, presents a survey of the structure and representation theory of semi groups. Volume II goes more deeply than was possible in volume I into

Regular ω-semigroups

  • W. Munn
  • Mathematics
    Glasgow Mathematical Journal
  • 1968
Let S be a semigroup whose set E of idempotents is non-empty. We define a partial ordering ≧ on E by the rule that e ≧ f and only if ef = f = fe. If E = {ei: i∈ N}, where N denotes the set of all

A Class of Irreducible matrix representations of an Arbitrary Inverse Semigroup

  • W. Munn
  • Mathematics
    Proceedings of the Glasgow Mathematical Association
  • 1961
By a ‘representation’ we shall mean throughout a representation by n × n matrices with entries from an arbitrary field. Elsewhere [9] the author has introduced the concept of a principal

Free inverse semigroups

This note announces a characterization of the free inverse semigroup I on a non-empty set X.