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Preprint Number 561
561. Amit Kuber
Grothendieck Rings of Theories of Modules
Submission date: 28 February 2013.
The model-theoretic Grothendieck ring of a first order structure, as defined by Krajicek and Scanlon, captures some combinatorial properties of the definable subsets of finite powers of the structure. In this paper we compute the Grothendieck ring, K_0(M), of a right R-module M, where R is any unital ring. As a corollary we prove a conjecture of Prest that K_0(M) is non-trivial, whenever M is non-zero. The main proof uses various techniques from the homology theory of simplicial complexes.
Mathematics Subject Classification: 03C60, 55U05, 16Y60, 20M25, 06A12
Keywords and phrases: Grothendieck ring; model theory; module; positive primitive formula; abstract simplicial complex, monoid ring.
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