September 2009 The model completion of the theory of modules over finitely generated commutative algebras
Moshe Kamensky
J. Symbolic Logic 74(3): 734-750 (September 2009). DOI: 10.2178/jsl/1245158083


We find the model completion of the theory modules over 𝔸, where 𝔸 is a finitely generated commutative algebra over a field K. This is done in a context where the field K and the module are represented by sorts in the theory, so that constructible sets associated with a module can be interpreted in this language. The language is expanded by additional sorts for the Grassmanians of all powers of Kⁿ, which are necessary to achieve quantifier elimination. The result turns out to be that the model completion is the theory of a certain class of “big” injective modules. In particular, it is shown that the class of injective modules is itself elementary. We also obtain an explicit description of the types in this theory.


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Moshe Kamensky. "The model completion of the theory of modules over finitely generated commutative algebras." J. Symbolic Logic 74 (3) 734 - 750, September 2009.


Published: September 2009
First available in Project Euclid: 16 June 2009

zbMATH: 1183.03028
MathSciNet: MR2548476
Digital Object Identifier: 10.2178/jsl/1245158083

Primary: 03C10
Secondary: 03C60

Keywords: modules,model completion,quantifier elimination

Rights: Copyright © 2009 Association for Symbolic Logic


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Vol.74 • No. 3 • September 2009
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