A New Universal Definition of \mathbbF_q [t] in \mathbbF_q (t)

2019/05/14 by Brian Tyrrell, Tyrrell, Brian
Computer Science · Mathematics · #Algebraic structures and combinatorial models #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.1905.05745

openalex publication_date 2019/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper gives a universal definition of \mathbbF_q [t] in \mathbbF_q (t) using 89 quantifiers, more direct than those that exist in the current literature. The language L_{rings, t} we consider here is the language of rings \0, 1, +, -, ⋅\ with an additional constant symbol t. We then modify this definition marginally to universally define \mathbbF_q [t] in \mathbbF_q (t) without parameters, using 90 quantifiers. We assume throughout that the characteristic of \mathbbF_q is odd.

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