\mathbbF_p((X)) is decidable as a module over the ring of additive polynomials

2018/06/08 by Gönenç Onay, Onay, Gönenç
Computer Science · Mathematics · #03C68 #11U05 #12J10 #12L05 #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Logic (math.LO) #Number Theory (math.NT) #Polynomial and algebraic computation #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1806.03123

openalex publication_date 2018/06/08 · openalex created_date 2018/10/26 · openalex updated_date 2026/07/28

Abstract

Let p be a prime number, K be the henselization of the rational functions over the finite field \mathbbF_p and R be the ring of additive polynomials over K. We show that the field of Laurent series over \mathbbF_p is decidable seen as an R-module. Moreover, we provide a recursively enumerable axiom system (satisfied by K) in the language of R-modules together with a unary predicate for the valuation ring, modulo which every positive primitive formula is equivalent to a universal formula. Consequently the R-module theory of the field of Laurent series is model-complete in this language and admits K as its prime model.

Citations

• Valued Modules over Skew Polynomial Rings 2

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