A general method for to decompose modular multiplicative inverse operators over Group of units.

• Cortés Vega, Luis A. ^[1]
  1. [1] Antofagasta University.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 37, Nº. 2, 2018, págs. 265-293
• Idioma: inglés
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• Resumen

  • In this article, the notion of modular multiplicative inverse operator (MMIO) ℐϱ : (Z/ϱZ)* → Z/ϱZ, ℐϱ (a) = a-1, where ϱ=b × d >3 with b, d ∈ N, is introduced and studied. A general method to decompose (MMIO) over group of units of the form (Z/ϱZ)* is also discussed through a new algorithmic functional version of Bezout's theorem. As a result, interesting decomposition laws for (MMIO)'s over (Z/ϱZ)* are obtained. Several numerical examples confirming the theoretical results are also reported.