Títol:
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Elements of algebraic geometry and the positive theory of partially commutative groups
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Autor/a:
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Casals-Ruiz, Montserrat; Kazachkov, Ilya v.; Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica
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Abstract:
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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. |
Matèries:
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-Grups abelians -Geometria algebraica -Models matemàtics |
Drets:
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open access
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https://creativecommons.org/licenses/by-nc-nd/2.5/ |
Tipus de document:
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Article Prepublicació |
Publicat per:
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Centre de Recerca Matemàtica
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Compartir:
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Uri:
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https://ddd.uab.cat/record/44079
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