Digit systems over commutative rings
Klaus Scheicher, Paul Surer, Jörg Μ. Thuswaldner, Christiaan E. van de Woestijne · International Journal of Number Theory · 2014
Let [Formula: see text] be a commutative ring with identity and [Formula: see text] be a polynomial. In the present paper we consider digit representations in the residue class ring [Formula: see text]. In particular, we are interested in the question whether each [Formula: see text] can be represented modulo P in the form e0+ e1x + ⋯ + ehxh, where the [Formula: see text] are taken from a fixed finite set of digits. This general concept generalizes both canonical number systems and digit systems over finite fields. Due to the fact that we do not assume that 0 is an element of the digit set and that P need not be monic, several new phenomena occur in this context.