Grothendieck Rings of Theories of Modules

Kuber, Amit (2013) Grothendieck Rings of Theories of Modules. [MIMS Preprint]

[img] PDF
Paper.pdf

Download (557kB)

Abstract

The model-theoretic Grothendieck ring of a first order structure, as defined by Krajic\v{e}k and Scanlon, captures some combinatorial properties of the definable subsets of finite powers of the structure. In this paper we compute the Grothendieck ring, $K_0(M_\mathcal R)$, of a right $R$-module $M$, where $\mathcal R$ 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.

Item Type: MIMS Preprint
Additional Information: Under review for Proceedings of the LMS.
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 03 Mathematical logic and foundations
MSC 2010, the AMS's Mathematics Subject Classification > 06 Order, lattices, ordered algebraic structures
MSC 2010, the AMS's Mathematics Subject Classification > 16 Associative rings and algebras
MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations
MSC 2010, the AMS's Mathematics Subject Classification > 55 Algebraic topology
Depositing User: Mr. Amit Kuber
Date Deposited: 18 Feb 2013
Last Modified: 20 Oct 2017 14:13
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1942

Actions (login required)

View Item View Item