Submission date: 22 September 2013.

Abstract:

We develop the basic theory of geometrically closed rings as a generalisation of algebraically closed fields, on the grounds of notions coming from positive model theory and affine algebraic geometry. For this purpose we consider several connections between finitely presented rings and ultraproducts, affine varieties and definable sets, and we introduce the key notion of an arithmetic theory as a purely algebraic version of coherent logic for rings.

Mathematics Subject Classification: 14A99

Keywords and phrases:

Full text arXiv 1309.5572: pdf, ps.