Submission date: 8 June 2018

Abstract:

Let R be the (non commutative-) ring of additive polynomials over the field K:=F_p(X)^h, the henselization of the field F_p(X). We show that the (right-) R-module theory of the field F_p((X)) is decidable. Moreover, we provide a recursively enumerable axiom system T_1 in the language L_O, the language of R-modules together with a predicate O for the valuation ring F_p[[X]] and show that every primitive positive formula is equivalent to a universal formula modulo T_1. The L_O-structure of F_p((X)) is also decidable and the L_O-theory of F_p((X)) is model-complete admitting K as its prime model.

Mathematics Subject Classification: 11U05, 12L05, 12J10, 03C68

Keywords and phrases:

Full text arXiv 1806.03123: pdf, ps.