03471nam 2200577 450 991048051360332120170822144224.01-4704-0616-0(CKB)3360000000465183(EBL)3114199(SSID)ssj0000889115(PQKBManifestationID)11932399(PQKBTitleCode)TC0000889115(PQKBWorkID)10875989(PQKB)11264215(MiAaPQ)EBC3114199(PPN)195418883(EXLCZ)99336000000046518320150417h20102010 uy 0engur|n|---|||||txtccrOn systems of equations over free partially commutative groups /Montserrat Casals-Ruiz, Ilya KazachkovProvidence, Rhode Island :American Mathematical Society,2010.©20101 online resource (153 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 212, Number 999'Volume 212, Number 999 (end of volume)."0-8218-5258-2 Includes bibliographical references and index.""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""Memoirs of the American Mathematical Society ;Volume 212, Number 999.Equations, AbelianAbelian groupsElectronic books.Equations, Abelian.Abelian groups.512.25Casals-Ruiz Montserrat903032Kazachkov IlyaMiAaPQMiAaPQMiAaPQBOOK9910480513603321On systems of equations over free partially commutative groups2018697UNINA