Decidability of Sub-theories of Polynomials over a Finite Field

Abstract. Let Fq be a finite field with q elements. We produce an (effective) elimination of quantifiers for the structure of the set of polynomials, Fq[t], of one variable, in the language which contains symbols for addition, multiplication by t, inequalities of degrees, divisibility of degrees by a positive integer and, for each d ∈ Fq[t], a symbol for divisibility by d. We discuss the possibility of extending our results to the structure which results if one includes a predicate for the relation “x is a power of t”.

• Type: Conference
• Year: 2009
• Where: CIE
• Authors: Alla Sirokofskich
• Keywords: Applied Computing, CIE 2009, Let Fq, Positive Integer, finite field