Digit systems over commutative rings - Scheicher, Klaus; Surer, Paul [UNESP]; Thuswaldner, Joerg M.; Van de Woestijne, Christiaan E. (World Scientific Publ Co Pte Ltd, 2014)
Let epsilon be a commutative ring with identity and P is an element of epsilon[x] be a polynomial. In the present paper we consider digit representations in the residue class ring epsilon[x]/(P). In particular, we are interested in the question whether each A is an element of epsilon[x]/(P) can be represented modulo P in the form e(0)+ e(1)x + ... + e(h)x(h), where the e(i) is an element of epsilon[x]/(P) 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.
Keywords: Canonical number systems; shift radix systems; digit systems