dc.contributor |
Centre de Recerca Matemàtica |
dc.contributor.author |
Casals-Ruiz, Montserrat |
dc.contributor.author |
Kazachkov, Ilya v. |
dc.date.accessioned |
2008-09-04T13:50:13Z |
dc.date.available |
2008-09-04T13:50:13Z |
dc.date.created |
2007-10 |
dc.date.issued |
2007-10 |
dc.identifier.uri |
http://hdl.handle.net/2072/9165 |
dc.format.extent |
44 |
dc.format.extent |
399850 bytes |
dc.format.mimetype |
application/pdf |
dc.language.iso |
eng |
dc.publisher |
Centre de Recerca Matemàtica |
dc.relation.ispartofseries |
Prepublicacions del Centre de Recerca Matemàtica;771 |
dc.rights |
Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús (http://creativecommons.org/licenses/by-nc-nd/2.5/es/) |
dc.subject.other |
Grups abelians |
dc.subject.other |
Geometria algebraica |
dc.subject.other |
Models matemàtics |
dc.title |
Elements of algebraic geometry and the positive theory of partially commutative groups |
dc.type |
info:eu-repo/semantics/preprint |
dc.subject.udc |
512 - Àlgebra |
dc.description.abstract |
The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group
over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets).
Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence,
the positive theory of an arbitrary partially commutative group is decidable. |