Research


2013

60. The structure of generalized inverse semigroups, with G. Kudryavtseva, accepted by Semigroup Forum for the edition in honour of John Howie.

59. Pseudogroups and their etale groupoids, with D. Lenz, Advances in Maths 244 (2013), 117--170.

58. The etale groupoid of an inverse semigroup as a groupoid of filters,  with S. W. Margolis and B. Steinberg,  J. Aust. Math. Soc. doi:10.1017/S144678871200050X.

57. Morita equivalence of inverse semigroups, with B. Afara, Periodica math Hung. 66 (2013), 119--130.

2012

56. Non-commutative Stone duality: inverse semigroups, topological groupoids and C*-algebras, IJAC 22, 1250058 (2012) DOI:10.1142/S0218196712500580.

55. Morita equivalence of semigroups with locally commuting idempotents, with B. Afara, Communications in Algebra 40, 1982--1996.

54. Strong representation of the polycyclic inverse monoids: cycles and atoms, with D. Jones,  Periodica Math. Hung. 64, 53-87.

2011

53. Characterizations of Morita equivalent inverse semigroups, with J. Funk and B. Steinberg,  J. Pure Appl. Algebra 215, 2262-2279.

52. Morita theory for semigroups with local units,  J. Pure Appl. Algebra 215, 455--470.

51. Generalized heaps, inverse semigroups and Morita equivalence, Algebra Universalis 66 (2011), 317--330.

2010

50. Compactable semilattices, Semigroup Forum 81, 187--199.

49. A non-commutative generalization of Stone duality,  J. Austral. Math. Soc. 88, 385--404.
2009

48. Primitive partial permutation representations of the polycyclic monoids and branching function systems, Periodica Math. Hung. 52, 189--207.

2008

47. Semigroups related to subshifts of graphs, Mathematics Studies of the Estonian Mathematical Society 3, (edited by V. Laan, S. Bulman-Fleming, R. Kaschek), 92--107.

46. A correspondence between a class of monoids and self-similar group actions I, Semigroup Forum 76, 489-517.

2007

45. The polycyclic monoids P_{n} and the Thompson groups V_{n,1}, Communications in algebra 35, 4068--4087.

44. A class of subgroups of Thompson's group V, Semigroup Forum 75, 241--252.

43. In McAlister's footsteps: a random ramble around the P-theorem, with S. Margolis  Proceedings of the International Conference on
Semigroups and Languages, Lisbon 2005, (eds Andre, Fernandes, Branco, Gomes, Fountain and Meakin) World Scientific, 2007, 145--163.

42. Orthogonal completions of the polycyclic monoids, Communications in Algebra 35,  1651--1660.

2006

41. A correspondence between balanced varieties and inverse monoids, Inter. J. Alg. and Computation 16, 887--924.

40. Expansions of inverse semigroups, with S. Margolis and B. Steinberg Journal of the Australian Mathematical Society 80, 205--228.

2005

39. Constructing ordered groupoids, Cah. Topol. Geom. Differ. Categ. 46, 123--138.

2004

38. Partial actions of groups, with J. Kellendonk,  International Journal of Algebra and Computation 14, 87--114.

37. Ordered groupoids and etendues, with B. Steinberg Cahiers de topologie et geometrie differentielle categoriques XLV, 82--108. 

36. One dimensional tiling semigroups, Semigroup Forum 68, 159--176.

35. Left cancellative categories and ordered groupoids, Semigroup Forum 68, 458--476.

34. Universal groups for point-sets and tilings, with J. Kellendonk J. Algebra 276, 462--492.

2002

33. E*-unitary inverse semigroups, in Semigroups, algorithms, automata and languages (eds G M S Gomes, J-E Pin, P V Silva) World Scientific, 195--214.

32. The homotopy theory of inverse semigroups, with J. Matthews and T. Porter International Journal of Algebra and Computation 12, 755--790.

2001

31. Rees matrix covers for a class of semigroups with locally commuting idempotents, with T. Khan Proc. Edinburgh Math. Soc. 44, 173--186.

30. Variants of regular semigroups, with T. Khan Semigroup Forum 62, 358--374.

2000

29. A characterisation of a class of semigroups with locally commuting idempotents, with T. Khan  Periodica Mathematica Hungarica 40, 85--107.

28. Tiling semigroups, with J. Kellendonk  Journal of Algebra 224, 140--150.

27. Enlargements and coverings by Rees matrix semigroups, with L. Marki Monatshefte fuer Mathematik 129, 191--195.

26. Rees matrix semigroups over semigroupoids and the structure of a class of abundant semigroups, Acta Scientiarum Mathematicarum 66, 517--540.

1999

25. An application of groupoids of fractions to inverse semigroups, with H. James Periodica Mathematica Hungarica 38 , 43--54.

24. The structure of 0-E-unitary inverse semigroups I: the monoid case,  Proc. Edinburgh Math. Soc. 42, 497--520.

23. Constructing inverse semigroups from category actions,  J. of Pure and Applied Algebra 137, 57--101.

1998

22. McAlister semigroups,  J. of Algebra 202, 276--294.

21. The Moebius inverse monoid,  J. of Algebra 200, 428--438.

20. An application of polycyclic monoids to rings,  with P. Hines Semigroup Forum 56, 146--149.

1997

19. Unit regular monoids,  with J. B. Hickey Proc. Royal Soc. Edinburgh 127A , 127--144.

1996

18. Enlargements of regular semigroups,  Proc. Edinburgh Math. Soc. 39, 425--460.

17. A class of actions of inverse semigroups,  J. of Algebra 179, 570--598.

1994

16. Almost factorisable inverse semigroups,  Glasgow Mathematical J. 36, 97--111.

15. Extending partial isomorphisms and McAlister's covering theorem ,  Semigroup Forum 48 , 18--27.

1993

14. A note on a paper of Joubert,  Semigroup Forum 47, 389--392.

13. Coverings and embeddings of inverse semigroups,  Proc. Edinburgh Math. Soc. 36, 399--419.

12. Congruences on ordered groupoids,  Semigroup Forum 47, 150--167.

11. An equivalence theorem for inverse semigroups,  Semigroup Forum 47, 7--14.

1992

10. The geometric theory of inverse semigroups II:  E-unitary covers of inverse semigroups,  J. Pure and Applied Algebra 83, 121--139.  

1991

9. Semigroups and ordered categories I: the reduced case,  J. of Algebra 141, 422--462.

1990

8. The geometric theory of inverse semigroups I: $E$-unitary inverse semigroups,  J. Pure and Applied Algebra 67, 151--177.

7. Rees matrix semigroups, Proc. Edinburgh Math. Soc. 33, 23--37.

1989

6. An order theoretic characterisation of  locally orthodox semigroups,  Semigroup Forum 39, 113--116.

1987

5. Rees matrix covers for a class of abundant semigroups,  Proc. Royal Soc. Edinburgh 107A, 109--120.

4. Abundant  Rees matrix semigroups,  J. Australian Math. Soc.  (Series~A)  42, 132--142.

3. The natural partial order on an abundant semigroup,  Proc. Edinburgh Math. Soc. 30, 169--186.

1986

2. The structure of type A semigroups, Quart. J. Maths. 37, 279--298.

1985

1. The translational hull of an adequate semigroup, with J. B. Fountain Semigroup Forum 32, 79--86.