LEADER 03471nam 2200577 450 001 9910480513603321 005 20170822144224.0 010 $a1-4704-0616-0 035 $a(CKB)3360000000465183 035 $a(EBL)3114199 035 $a(SSID)ssj0000889115 035 $a(PQKBManifestationID)11932399 035 $a(PQKBTitleCode)TC0000889115 035 $a(PQKBWorkID)10875989 035 $a(PQKB)11264215 035 $a(MiAaPQ)EBC3114199 035 $a(PPN)195418883 035 $a(EXLCZ)993360000000465183 100 $a20150417h20102010 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aOn systems of equations over free partially commutative groups /$fMontserrat Casals-Ruiz, Ilya Kazachkov 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2010. 210 4$dİ2010 215 $a1 online resource (153 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 212, Number 999 300 $a'Volume 212, Number 999 (end of volume)." 311 $a0-8218-5258-2 320 $aIncludes bibliographical references and index. 327 $a""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"" 327 $a""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"" 327 $a""6.5. Regular case""""Chapter 7. The finite tree T0() and minimal solutions""; ""7.1. Automorphisms""; ""7.2. The finite subtree T0()""; ""7.3. Paths p(H) are in T0()""; ""Chapter 8. From the coordinate group GR(*) to proper quotients: the decomposition tree Tdec and the extension tree Text""; ""8.1. The decomposition tree Tdec()""; ""8.2. Example""; ""8.3. The extension tree Text()""; ""Chapter 9. The solution tree T`39`42`""613A``45`47`""603Asol() and the main theorem""; ""9.1. Example""; ""Bibliography""; ""Index""; ""Glossary of notation"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 212, Number 999. 606 $aEquations, Abelian 606 $aAbelian groups 608 $aElectronic books. 615 0$aEquations, Abelian. 615 0$aAbelian groups. 676 $a512.25 700 $aCasals-Ruiz$b Montserrat$0903032 702 $aKazachkov$b Ilya 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480513603321 996 $aOn systems of equations over free partially commutative groups$92018697 997 $aUNINA