منابع مشابه
Deenability of Geometric Properties in Algebraically Closed Fields Deenability of Geometric Properties in Algebraically Closed Fields Deenability of Geometric Properties in Algebraically Closed Fields
We prove that there exists no sentence F of the language of rings with an extra binary predicat I satisfying the following property for every de nable set X C X is connected if and only if C X j F where I is interpreted by X We conjecture that the same result holds for the closed subsets of C We prove some results motivated by this conjecture
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These notes are intended to accompany the tutorial series ‘Model theory of algebraically closed valued fields’ in the Workshop ‘An introduction to recent applications of model theory’, Cambridge March 29–April 8, 2005. They do not contain any new results, except for a slightly new method of exposition, due to Lippel, of parts of the proof of elimination of imaginaries, in Sections 8 and 9. They...
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The classical McKay correspondence for finite subgroups G of SL(2,C) gives a bijection between isomorphism classes of nontrivial irreducible representations of G and irreducible components of the exceptional divisor in the minimal resolution of the quotient singularity A2C/G. Over non algebraically closed fields K there may exist representations irreducible over K which split over K. The same i...
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We give a presentation of the construction of motivic integration, that is, a homomorphism between Grothendieck semigroups that are associated with a first-order theory of algebraically closed valued fields, in the fundamental work of Hrushovski and Kazhdan [12]. We limit our attention to a simple major subclass of V -minimal theories of the form ACVF S , that is, the theory of algebraically cl...
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Let k be an uncountable algebraically closed field and let A be a countably generated left Noetherian k-algebra. Then we show that A⊗k K is left Noetherian for any field extension K of k. We conclude that all subfields of the quotient division algebra of a countably generated left Noetherian domain over k are finitely generated extensions of k. We give examples which show that A⊗k K need not re...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1985
ISSN: 0021-8693
DOI: 10.1016/0021-8693(85)90177-2