Semigroups and Formal Languages: Proceedings of the International Conference, in Honour of the 65th Birthday of Donald B. Mcalister

Jorge M. Andre, Vitor H. Fernandes, Mario J. J. Branco, Gracinda M. S. Gomes, John Fountain9789812707383, 981-270-738-7

This festschrift volume in honour of Donald B McAlister on the occasion of his 65th birthday presents papers from leading researchers in semigroups and formal languages. The contributors cover a number of areas of current interest: from pseudovarieties and regular languages to ordered groupoids and one-relator groups, and from semigroup algebras to presentations of monoids and transformation semigroups. The papers are accessible to graduate students as well as researchers seeking new directions for future work.

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Table of contents :
Contents……Page 10
Preface……Page 6
1. Introduction……Page 12
2. Preliminaries……Page 13
3. Membership and word problems……Page 14
4. Connection with automatic semigroups……Page 17
References……Page 19
1. Introduction……Page 20
2. How we are led to systems of equations……Page 21
3. Simplifications……Page 25
4. Further simplifications for the case of R……Page 26
5. Complete reducibility of R……Page 27
6. General strategy of the proof……Page 29
Appendix……Page 32
References……Page 34
1. Introduction……Page 37
2. Proof of the Main Theorem……Page 39
3. Example……Page 46
References……Page 48
1. Operations on languages……Page 50
2. Rational and recognisable languages……Page 51
3.1. Star-free languages……Page 53
3.2. The star-height problem……Page 55
4. Concatenation hierarchies……Page 56
5. Back to the star-height problem……Page 62
6. Shuffle product……Page 65
References……Page 66
1. Introduction……Page 68
2. Solving systems modulo pseudovarieties of abelian groups……Page 71
2.1. Proof of Theorem 1.1……Page 74
2.2. Proof of Theorem 1.2……Page 75
Bibliography……Page 76
1. Introduction……Page 77
2. Mathematical Preliminaries and Notations……Page 78
3. Holonomy Decomposition Theorem……Page 82
4.1. Representation……Page 84
4.2. The Extended Set of Images……Page 85
4.3. Subduction, Equivalence Relation, and the Tiling Picture……Page 86
4.4. Number of Levels……Page 88
4.5. Number of States……Page 89
4.6. Holonomy Group Components……Page 90
5. Examples of Decomposition……Page 92
6. Conclusion and Future Work……Page 93
References……Page 94
1. Introduction……Page 95
2. Levelling ordered groupoids……Page 97
2.1. Incompressible ordered groupoids……Page 100
2.1.1. E–unitary inverse semigroups……Page 101
2.2. –transitive ordered groupoids……Page 102
3. Groupoids acting on posets……Page 104
4. The P–theorem……Page 105
5.1. A Clifford semigroup……Page 109
5.3. HNN extensions……Page 110
References……Page 111
1. Introduction……Page 112
2. Proof of Theorem 1.1……Page 114
References……Page 121
Introduction……Page 122
1. Proof of the Theorem……Page 124
2.1. Words……Page 127
2.2. Diagrams……Page 129
3. Piece configurations of 1-corner regions and 2-corner regions……Page 131
4. Proposition 4.1 and its proof……Page 135
References……Page 139
1. Introduction……Page 140
2. Wreath Products, Division and Complexity……Page 142
3. Triangular Matrix Semigroups……Page 146
4. Decompositions for Triangular Matrix Semigroups……Page 148
5. Comparison with Depth Decomposition……Page 152
References……Page 154
1. A primer on categories and inverse semigroups……Page 156
2. The P-theorem……Page 159
3. Partial group actions……Page 162
4. Ordered groupoids……Page 164
5. Extensions of semilattices by groups, the derived category and global semigroup theory……Page 167
6. Cancellative categories……Page 170
References……Page 171
Introduction……Page 175
1. The variety A2 and a decomposition of its subvariety lattice into intervals……Page 177
2. Regular elements in semigroups from A2 and their representation by words……Page 180
3. Kublanovskii’s lemma and the scheme of its usage……Page 186
4. Main results……Page 190
References……Page 196
1. Introduction……Page 199
2.1. Presentations and rewriting systems……Page 201
2.2. About 2-complexes……Page 202
2.3. The Squier complex……Page 203
3. A general presentation for a subsemigroup……Page 204
4. A general trivializer for a subsemigroup……Page 207
5. An application to bands of monoids……Page 208
References……Page 214
1. Introduction……Page 216
2. The free monogenic semilatticed inverse semigroup……Page 218
3. Totally ordered !-regular semigroups…….Page 220
4. E-unitary inverse semigroups…….Page 222
5. Semidirect product embeddings……Page 224
References……Page 228
1. Introduction……Page 230
2. Isomorphisms between transformation semigroups……Page 231
3. Isomorphisms between linear transformation semigroups……Page 234
4. Isomorphisms between Baer-Levi semigroups……Page 236
References……Page 239
1. The McAlister monoid Mx……Page 241
2. The contracted monoid algebra of MX……Page 248
References……Page 250
1. Introduction……Page 251
2. Relative monoid presentations……Page 253
3. The Squier complex of a relative monoid presentation……Page 254
4. F-G-sequences……Page 257
5. Application……Page 263
References……Page 265
1. Introduction……Page 266
2. Preliminaries……Page 267
3. Varieties of homomorphisms onto abelian groups……Page 270
4. Pseudovarieties of finite homomorphisms onto abelian groups……Page 272
5. Corresponding languages……Page 273
References……Page 276
1. Preliminaries……Page 277
2.1. First approach……Page 279
2.2. Second approach……Page 280
3.1. First approach……Page 282
3.2. Second approach……Page 283
References……Page 287