Direct factors of polynomial rings over finite fields
An asymptotic formula is derived for the total number of polynomials of degree n in an arbitrary direct factor of the set G of all monic polynomials in one unknown over a finite field with q elements. A direct factor of G is a subset \(B_ 1\) of G such that for some subset \(B_ 2\) of G, every polynomial w in G has a unique factorization of the form \(w=b_ 1b_ 2\), where \(b_ i\in B_ i\). The asymptotic formula is given as \(c_ 1q^ n\), where \(c_ 1\) is a constant depending on \(B_ 1\).
scientific article; zbMATH DE number 3948426