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


  • Luis A. Cortés Vega Antofagasta University.


Descomposition laws, Group of units, Bezout’s theorem, Modular multiplicative inverse operator, Algorithmic functional technique, Chinese remainder theorem


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

ϱ : (Z/ϱZ)* → Z/ϱZ,ϱ (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.

Author Biography

Luis A. Cortés Vega, Antofagasta University.

Department of Mathematics.


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How to Cite

L. A. Cortés Vega, “A general method for to decompose modular multiplicative inverse operators over Group of units.”, Proyecciones (Antofagasta, On line), vol. 37, no. 2, pp. 265-293, Jun. 2018.