Artigo
Digit systems over commutative rings
Registro en:
International Journal Of Number Theory. Singapore: World Scientific Publ Co Pte Ltd, v. 10, n. 6, p. 1459-1483, 2014.
1793-0421
10.1142/S1793042114500389
WOS:000341012700008
Autor
Scheicher, Klaus
Surer, Paul [UNESP]
Thuswaldner, Joerg M.
Van de Woestijne, Christiaan E.
Resumen
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. Austrian Science Foundation (FWF) national research network "Analytic combinatorics and probabilistic number theory" Univ Nat Resources & Appl Life Sci, Inst Math, A-1180 Vienna, Austria Univ Estadual Paulista UNESP, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil Univ Leoben, Chair Math & Stat, A-8700 Leoben, Austria Univ Estadual Paulista UNESP, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil Austrian Science Foundation (FWF)S9606 Austrian Science Foundation (FWF)S9610 national research network Analytic combinatorics and probabilistic number theoryFWF-S96