
Peter Trotter 


Peter Trotter's home page
Research interests
Semigroups. Congruences on regular semigroups. Varieties of completely
regular semigroups and of inverse semigroups, evarieties and
pseudovarieties.
Publications
1. Soluble semigroups, J. Austral. Math. Soc. 13 (1971),114118
2. A Class of semigroups embeddable in groups, Semigroup Forum 5
(1972),
113
3. Congruencefree inverse semigroups, Semigroup Forum 9 (1974),
109116
4. Congruencefree regular semigroups with zero, Semigroup Forum 12
(1976), 15
5. Exponential delta semigroups, Semigroup Forum 12 (1976), 313331
6. (With T Tamura) Completely semisimple inverse delta semigroups
admitting
principal series, Pacific J. Math. 68 (1977), 515525
7. Cancellative simple semigroups and groups, Semigroup Forum 14
(1977),
189198
8. Congruencefree right simple semigroups, J. Austral. Math. Soc.
24 (1977), 103111
9. Normal partitions of idempotents of regular semigroups, J. Austral.
Math. Soc. 26 (1978), 110114
10. Ideals in Z[x,y], Acta. Math. Sci Hungar. 32 (1978), 6373
11. Free objects in some categories of semigroups, Proc. of the
conference
on semigroups in honour of A H Clifford, Tulane University (1978),
188192
12. Non existence of coreflections and coproducts in some categories
of semigroups, Proc. Amer. Math. Soc. 80 (1980), 1014
13. Projectives in some categories of semigroups, Semigroups, Ed. T
E Hall, P R Jones, G B Preston, Academic Press, New York (1980),
!33145
14. Congruences on regular and completely regular semigroups, J.
Austral.
Math. Soc. 32 (1982), 388398
15. Projectives of finite regular semigroups, J. Algebra 77 (1982),
4961
16. Projective inverse semigroups, Semigroup Forum 26 (1983), 167190
17. The least orthodox congruence on a completely regular semigroup,
Indian J. Math. 25 (1983), 125133
18. Free completely regular semigroups, Glasgow Math. J. 25 (1984),
241254
19. (With F. J. Pastijn) Lattices of completely regular semigroup
varieties,
Pacific J. Math. 119 (1985), 191214
20. A nonsurjective endomorphism of bands, Algebra Universalis 22
(1986), 109116
21. (With N. R. Reilly) Properties of relatively free inverse
semigroups,
Trans. Amer. Math. Soc. 294 (1986), 243262
22. Relatively free inverse semigroups, Quart. J. Math. Oxford (2)
37 (1986), 357374
23. Injectives in varieties of completely simple semigroups, Semigroup
Forum 33 (1986), 4755
24. On a problem of Pastijn and Petrich, Semigroup Forum 34 (1986),
249252
25. (With F. J. Pastijn) Residual finiteness in completely regular
semigroup varieties, Semigroup Forum 37 (1988), 127147
26. Varieties of completely regular semigroups: their injectives,
Lecture
Notes in Mathematics 1320, SpringerVerlag, Berlin (1988), 372379
27. Free generators in relatively free completely regular semigroups,
Proc. Royal Soc. Edinburgh 109A (1988), 329339
28. Subdirect decompositions of the lattice of varieties of completely
regular semigroups, Bull. Austral. Math. Soc. 39 (1989), 343351
29. Injectives in varieties of completely regular semigroups, J. Pure
and Applied Algebra 58 (1989), 289303
30. Relatively free bands of groups, Acta Sci. Math. Szeged 53 (1989),
1931
31. (With P. R. Jones) The Howson property for free inverse semigroups,
Simon Stevin 63 (1989), 277284
32. (With P. R. Jones) The Howson property in varieties of completely
regular semigroups, Simon Stevin 63 (1989), 285294
33. Congruence extensions in regular semigroups, J. Algebra 137 (1991),
166179
34. The word problem for relatively free completely regular semigroups,
Monoids and semigroups with applications, Ed. J. Rhodes, World
Scientific
(1991), 198205
35. Unary semigroup joins of varieties of inverse and completely
regular
semigroups, Monash conference on semigroup theory, Ed. T. E. Hall, P.
R.
Jones, J. C. Meakin, World Scientific (1991), 296305
36. (With F. J. Pastijn) Free bands of abelian groups, Proc. London
Math. Soc, 63 (1991), 344370
37. (With P. R. Jones) Joins of inverse and band varieties,
International
J. Algebra and Computation, 1 (1991), 371385
38. A nonlocal variety of completely regular monoids with a member
of complexity 2, Semigroups with applications, Ed. J. M. Howie, W. D.
Munn,
H. J. Weinert, World Scientific (1992), 162169
39. (With Z. Jiang) Covers for regular semigroups, SEA Bull. Math.
18 (1994), 157161
40. (With P. R. Jones) Locality of DS and associated varieties, J.
Pure and Applied Algebra, 104 (1995), 275301
41. (With M. Volkov) The finite basis problem in the pseudovariety
joins of aperiodic semigroups with groups, Semigroup Forum, 52 (1996),
8391
42. Covers for regular semigroups and an application to complexity,
J. Pure and Applied Algebra, 105 (1995), 319328
43. Evarieties of regular semigroups, Semigroups, automata and
languages,
Ed. J. Almeida, G. M. S. Gomes P. V. Silva, World Scientific (1996),
247262
44. (With P. R. Jones) Semidirect products of regular semigroups,
Trans.
Amer. Math. Soc. 349 (1997), 42654310
45. (With T. E. Hall, S. I. Kublanovskii, S. Margolis, M. V. Sapir)
Algorithmic problems for finite groups and finite 0simple semigroups,
J. Pure and Applied Algebra, 119 (1997), 7596
46. (With p. Weil) The lattice of pseudovarieties of idempotent
semigroups
and a nonregular analogue, Algebra Universalis 37 (1997), 491526
47. (With F. Pastijn) Complete congruences on lattices of varieties
and of pseudovarieties, Int. J. Algebra and Computation, 8 (1998),
171201
48. (With K. Auinger) Pseudovarieties, regular semigroups and
semidirect
products, J. London Math. Soc., 58 (1998), 284296
49. The lattices of pseudovarieties of DA and B, Semigroups and
Applications,
Ed. JM Howie, N Ruskuc, World Scientific (1998), 215228
50. On bases of identities of semidirect products of varieties of
semigroups,
Semigroups with applications including semigroup rings, Ed. S
Kublanovsky,
A Mikhalev, P Higgins, J Ponizovskii, St. Petersburg (1999), 401410
51. (With Z. Jiang) Universal aspects of regular *semigroups,
Algebraic
Engineering, Ed. CL Nehaniv, M Ito, World Scientific (1999), 437447
52. (With G. Churchill) A unified approach to biidentities in
evarieties,
Semigroup Forum, 60 (2000), 208230
53. (With J Almeida) Hyperdecidability of pseudovarieties of
orthogroups,
Glasgow Math. J. , 43 (2001), 6783
54. (With J Almeida) The pseudoidentity problem and reducibility for
completely regular semigroups, Bull. Austral. Math. Soc., 63 (2001),
407433.
55. (With K Auinger) A syntactic approach to covers for Edense
semigroups
over group varieties, Mathematika, 48 (2001)231245.
56. Regular semigroups, The Concise Handbook of Algebra, Ed. AV
Mikhalev,
G Pilz, Kluwer (2002), 3538.
57. Inverse semigroups, The Concise Handbook of Algebra, Ed. AV
Mikhalev,
G Pilz, Kluwer (2002), 4246.
58. (With G Pilz and L Shevrin) Applications of semigroups, The Concise
Handbook of Algebra, Ed. AV Mikhalev, G Pilz, Kluwer (2002), 6670.
59. Completely regular semigroups by Mario Petrich and Norman Reilly
(Book Review), Semigroup Forum 64 (2002) 333336.
60. Decidability problems in finite semigroups, Semigroups,
Algorithms,
Automata and Languages, Ed. GMS Gomes, JE Pin, PV Silva, World
Scientific
(2002), 501515.
61. (With K Auinger) A syntactic approach to covers for Edense
semigroups
over group varieties, Mathematika, 48 (2001)231245.
62. (With DF Cowan, NR Reilly and MV Volkov) The finite basis problem
for quasivarieties and pseudovarieties generated by regular
semigroups
1. Quasivarieties generated by regular semigroups, J. Algebra, 267
(2003) 635653.
63.(With Fang Li) Concise Encyclopedia of Supersymmetry and
Noncommutative Structures in Mathematics and Physics, Ed. S Duplij, W
Siegel, J Bagger, Kluwer (2004), 9293, 97, 209, 502503.
64. (With A Kelarev) A combinatorial property of languages and monoids,
Proc. internat. colloquium on words, languages and combinatorics, Ed. T
Imoaka, M Ito, Kyoto, to appear.
Address
Dr P G Trotter
School of Mathematics and Physics, University of Tasmania
GPO Box 252C37, Hobart, Tasmania 7001, Australia
PHONE: (03) 6226 2450
FAX: (03) 6226 2867
EMAIL: Peter.Trotter@utas.edu.au





