Digit Systems over commutative rings

Sobre o artigo

Resumo

Seja um anel comutativo com identidade e P∈[x] um polinômio. Neste artigo consideramos representações de dígitos no anel quociente [x]/(P). Especialmente nós interessamo-nos em saber se cada um A∈[x]/(P) possui uma representação módulo P da forma e0+e1X+^…+ehXh, em que ei∈[x]/(P) são elementos de um conjunto fixo de dígitos. Esse conceito geral generaliza tanto sistemas canônicos de numeração quanto sistemas de dígitos sobre corpos finitos. Como nós não assumimos que 0 seja um elemento do conjunto de dígitos e P não precisa ser mônico, alguns novos fenômenos ocorrem neste contexto.

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Links

International Journal of Number Theory
Pré-publicação no arXiv.org
Fundação Austríaca de Ciência (FWF)
Rede national de pesquisa (NFN) S9600