On systems of equations over free partially commutative groups / / Montserrat Casals-Ruiz, Ilya Kazachkov

• Record Nr.: UNINA9910828111903321
• Autore: Casals-Ruiz Montserrat
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2010; ©2010
• ISBN: 1-4704-0616-0
• Descrizione fisica: 1 online resource (153 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 212, Number 999
• Disciplina: 512.25
• Soggetti: Equations, Abelian; Abelian groups
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: 'Volume 212, Number 999 (end of volume)."
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: ""Contents""; ""List of Figures""; ""Chapter 1. Introduction""; ""Chapter 2. Preliminaries""; ""2.1. Graphs and relations""; ""2.2. Elements of algebraic geometry over groups""; ""2.3. Formulas in the languages LA and LG""; ""2.4. First order logic and algebraic geometry""; ""2.5. Partially commutative groups""; ""2.6. Partially commutative monoids and DM-normal forms""; ""Chapter 3. Reducing systems of equations over G to constrained generalised equations over F""; ""3.1. Definition of (constrained) generalised equations""; ""3.2. Reduction to generalised equations: from partially commutative groups to monoids""""3.3. Reduction to generalised equations: from partially commutative monoids to free monoids""; ""3.4. Example""; ""Chapter 4. The process: construction of the tree T""; ""4.1. Preliminary definitions""; ""4.2. Elementary transformations""; ""4.3. Derived transformations""; ""4.4. Construction of the tree T()""; ""Chapter 5. Minimal solutions""; ""Chapter 6. Periodic structures""; ""6.1. Periodic structures""; ""6.2. Example""; ""6.3. Strongly singular and singular cases""; ""6.4. Example""; ""6.5. Regular case""""Chapter 7. The finite tree T0() and minimal solutions""; ""7.1. Automorphisms""; ""7.2. The finite subtree T0()""; ""7.3. Paths p(H) are in T0()""; ""Chapter 8. From the coordinate group GR(*) to proper quotients: the decomposition tree Tdec and the ; extension tree Text""; ""8.1. The decomposition tree Tdec()""; ""8.2. Example""; ""8.3. The extension tree Text()""; ""Chapter 9. The solution tree T`39`42`""613A``45`47`""603Asol() and the main theorem""; ""9.1. Example""; ""Bibliography""; ""Index""; ""Glossary of notation""