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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.37 no.2 Antofagasta June 2018

http://dx.doi.org/10.4067/S0716-09172018000200265 

Articles

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

Luis A. Cortés Vega1 

1Universidad de Antofagasta, Department of Mathematics, Antofagasta, Chile. E-mail: luis.cortes@uantof.cl

Abstract:

In this article, the notion of modular multiplicative inverse operator (MMIO):

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 (ZZ)* is also discussed through a new algorithmic functional version of Bezout's theorem. As a result, interesting decomposition laws for (MMIO)'s over (ZZ)* are obtained. Several numerical examples confirming the theoretical results are also reported.

Keywords : Descomposition laws; group of units; Bezout's theorem; modular multiplicative inverse operator; algorithmic functional technique; Chinese remainder theorem.

Subjclass [2010] : Primary 11P83; 11A05; 11A07; 68W10 Secondary 68U20; 68W35; 97N70; 11T55; 68R01.

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

Acknowledgments:

I am especially indebted to professor Dr. Alvaro Restuccia, academic of Department of Physics of the Antofagasta University by their support, via fondecyt Grant #1161192, Chile. The referee made valuable comments, for which the present author is grateful. The current paper is a revised and expanded version of the original submission. I also want to thank to Professor Javier Silva Rojas for his invaluable help.

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Received: July 2017; Accepted: October 2017

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