## 48 Citations

### Inverse Semigroups and Extensions of Groups by Semilattices

- Mathematics
- 2003

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

- Mathematics
- 1982

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

- MathematicsInt. J. Algebra Comput.
- 1999

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

- MathematicsJournal of the Australian Mathematical Society
- 1976

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

- MathematicsGlasgow Mathematical Journal
- 1975

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

- MathematicsGlasgow Mathematical Journal
- 1993

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

- MathematicsJournal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
- 1999

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

- MathematicsInt. J. Algebra Comput.
- 1999

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

- MathematicsProceedings 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

- Mathematics
- 2005

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

## References

SHOWING 1-10 OF 20 REFERENCES

### Proper ordered inverse semigroups.

- Mathematics
- 1965

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

- Mathematics
- 1968

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

- MathematicsCanadian Journal of Mathematics
- 1968

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

- MathematicsProceedings 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

- Mathematics
- 1964

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

- MathematicsGlasgow 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

- MathematicsProceedings 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

- Mathematics
- 1972

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