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Peter Trotter |
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Peter Trotter's home page
Research interests
Semigroups. Congruences on regular semigroups. Varieties of completely
regular semigroups and of inverse semigroups, e-varieties and
pseudovarieties.
Publications
1. Soluble semigroups, J. Austral. Math. Soc. 13 (1971),114-118
2. A Class of semigroups embeddable in groups, Semigroup Forum 5
(1972),
1-13
3. Congruence-free inverse semigroups, Semigroup Forum 9 (1974),
109-116
4. Congruence-free regular semigroups with zero, Semigroup Forum 12
(1976), 1-5
5. Exponential delta semigroups, Semigroup Forum 12 (1976), 313-331
6. (With T Tamura) Completely semisimple inverse delta semigroups
admitting
principal series, Pacific J. Math. 68 (1977), 515-525
7. Cancellative simple semigroups and groups, Semigroup Forum 14
(1977),
189-198
8. Congruence-free right simple semigroups, J. Austral. Math. Soc.
24 (1977), 103-111
9. Normal partitions of idempotents of regular semigroups, J. Austral.
Math. Soc. 26 (1978), 110-114
10. Ideals in Z[x,y], Acta. Math. Sci Hungar. 32 (1978), 63-73
11. Free objects in some categories of semigroups, Proc. of the
conference
on semigroups in honour of A H Clifford, Tulane University (1978),
188-192
12. Non existence of coreflections and coproducts in some categories
of semigroups, Proc. Amer. Math. Soc. 80 (1980), 10-14
13. Projectives in some categories of semigroups, Semigroups, Ed. T
E Hall, P R Jones, G B Preston, Academic Press, New York (1980),
!33-145
14. Congruences on regular and completely regular semigroups, J.
Austral.
Math. Soc. 32 (1982), 388-398
15. Projectives of finite regular semigroups, J. Algebra 77 (1982),
49-61
16. Projective inverse semigroups, Semigroup Forum 26 (1983), 167-190
17. The least orthodox congruence on a completely regular semigroup,
Indian J. Math. 25 (1983), 125-133
18. Free completely regular semigroups, Glasgow Math. J. 25 (1984),
241-254
19. (With F. J. Pastijn) Lattices of completely regular semigroup
varieties,
Pacific J. Math. 119 (1985), 191-214
20. A non-surjective endomorphism of bands, Algebra Universalis 22
(1986), 109-116
21. (With N. R. Reilly) Properties of relatively free inverse
semigroups,
Trans. Amer. Math. Soc. 294 (1986), 243-262
22. Relatively free inverse semigroups, Quart. J. Math. Oxford (2)
37 (1986), 357-374
23. Injectives in varieties of completely simple semigroups, Semigroup
Forum 33 (1986), 47-55
24. On a problem of Pastijn and Petrich, Semigroup Forum 34 (1986),
249-252
25. (With F. J. Pastijn) Residual finiteness in completely regular
semigroup varieties, Semigroup Forum 37 (1988), 127-147
26. Varieties of completely regular semigroups: their injectives,
Lecture
Notes in Mathematics 1320, Springer-Verlag, Berlin (1988), 372-379
27. Free generators in relatively free completely regular semigroups,
Proc. Royal Soc. Edinburgh 109A (1988), 329-339
28. Subdirect decompositions of the lattice of varieties of completely
regular semigroups, Bull. Austral. Math. Soc. 39 (1989), 343-351
29. Injectives in varieties of completely regular semigroups, J. Pure
and Applied Algebra 58 (1989), 289-303
30. Relatively free bands of groups, Acta Sci. Math. Szeged 53 (1989),
19-31
31. (With P. R. Jones) The Howson property for free inverse semigroups,
Simon Stevin 63 (1989), 277-284
32. (With P. R. Jones) The Howson property in varieties of completely
regular semigroups, Simon Stevin 63 (1989), 285-294
33. Congruence extensions in regular semigroups, J. Algebra 137 (1991),
166-179
34. The word problem for relatively free completely regular semigroups,
Monoids and semigroups with applications, Ed. J. Rhodes, World
Scientific
(1991), 198-205
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), 296-305
36. (With F. J. Pastijn) Free bands of abelian groups, Proc. London
Math. Soc, 63 (1991), 344-370
37. (With P. R. Jones) Joins of inverse and band varieties,
International
J. Algebra and Computation, 1 (1991), 371-385
38. A non-local 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), 162-169
39. (With Z. Jiang) Covers for regular semigroups, SEA Bull. Math.
18 (1994), 157-161
40. (With P. R. Jones) Locality of DS and associated varieties, J.
Pure and Applied Algebra, 104 (1995), 275-301
41. (With M. Volkov) The finite basis problem in the pseudovariety
joins of aperiodic semigroups with groups, Semigroup Forum, 52 (1996),
83-91
42. Covers for regular semigroups and an application to complexity,
J. Pure and Applied Algebra, 105 (1995), 319-328
43. E-varieties of regular semigroups, Semigroups, automata and
languages,
Ed. J. Almeida, G. M. S. Gomes P. V. Silva, World Scientific (1996),
247-262
44. (With P. R. Jones) Semidirect products of regular semigroups,
Trans.
Amer. Math. Soc. 349 (1997), 4265-4310
45. (With T. E. Hall, S. I. Kublanovskii, S. Margolis, M. V. Sapir)
Algorithmic problems for finite groups and finite 0-simple semigroups,
J. Pure and Applied Algebra, 119 (1997), 75-96
46. (With p. Weil) The lattice of pseudovarieties of idempotent
semigroups
and a non-regular analogue, Algebra Universalis 37 (1997), 491-526
47. (With F. Pastijn) Complete congruences on lattices of varieties
and of pseudovarieties, Int. J. Algebra and Computation, 8 (1998),
171-201
48. (With K. Auinger) Pseudovarieties, regular semigroups and
semidirect
products, J. London Math. Soc., 58 (1998), 284-296
49. The lattices of pseudovarieties of DA and B, Semigroups and
Applications,
Ed. JM Howie, N Ruskuc, World Scientific (1998), 215-228
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), 401-410
51. (With Z. Jiang) Universal aspects of regular *-semigroups,
Algebraic
Engineering, Ed. CL Nehaniv, M Ito, World Scientific (1999), 437-447
52. (With G. Churchill) A unified approach to biidentities in
e-varieties,
Semigroup Forum, 60 (2000), 208-230
53. (With J Almeida) Hyperdecidability of pseudovarieties of
orthogroups,
Glasgow Math. J. , 43 (2001), 67-83
54. (With J Almeida) The pseudoidentity problem and reducibility for
completely regular semigroups, Bull. Austral. Math. Soc., 63 (2001),
407-433.
55. (With K Auinger) A syntactic approach to covers for E-dense
semigroups
over group varieties, Mathematika, 48 (2001)231-245.
56. Regular semigroups, The Concise Handbook of Algebra, Ed. AV
Mikhalev,
G Pilz, Kluwer (2002), 35-38.
57. Inverse semigroups, The Concise Handbook of Algebra, Ed. AV
Mikhalev,
G Pilz, Kluwer (2002), 42-46.
58. (With G Pilz and L Shevrin) Applications of semigroups, The Concise
Handbook of Algebra, Ed. AV Mikhalev, G Pilz, Kluwer (2002), 66-70.
59. Completely regular semigroups by Mario Petrich and Norman Reilly
(Book Review), Semigroup Forum 64 (2002) 333-336.
60. Decidability problems in finite semigroups, Semigroups,
Algorithms,
Automata and Languages, Ed. GMS Gomes, J-E Pin, PV Silva, World
Scientific
(2002), 501-515.
61. (With K Auinger) A syntactic approach to covers for E-dense
semigroups
over group varieties, Mathematika, 48 (2001)231-245.
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) 635-653.
63.(With Fang Li) Concise Encyclopedia of Supersymmetry and
Noncommutative Structures in Mathematics and Physics, Ed. S Duplij, W
Siegel, J Bagger, Kluwer (2004), 92-93, 97, 209, 502-503.
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 252C-37, Hobart, Tasmania 7001, Australia
PHONE: (03) 6226 2450
FAX: (03) 6226 2867
EMAIL: Peter.Trotter@utas.edu.au
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