Decidability of the theory of modules over commutative valuation domains

doi:10.1016/j.apal.2006.09.002

Annals of Pure and Applied Logic

Volume 145, Issue 3, March 2007, Pages 258-275

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Abstract

We prove that, if $V$ is an effectively given commutative valuation domain such that its value group is dense and archimedean, then the theory of all $V$ -modules is decidable.

Keywords

Theory of modules

Commutative valuation domain

Decidability

Ziegler spectrum