A new decomposition law for inverses modular multiplicative on (ℤ/ϱℤ)

• Published in: Journal of physics. Conference series Vol. 1730; no. 1; pp. 12130 - 12134
• Main Author: Cortés-Vega, Luis A.
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.01.2021
• Subjects: Algorithms; Computer architecture; Data structures; Decomposition; Operators (mathematics); Particle physics; Physics
• ISSN: 1742-6588; 1742-6596
• DOI: 10.1088/1742-6596/1730/1/012130

In modular arithmetic, we find a valuable concept, the so-called "modular multiplicative inverse" (symbolized by MMI). In precise words, if ℤ/ϱℤ denoted the residue system modulo ϱ, the (MMI) of a ∈ ℤ/ϱℤ, if it exists, is a−1 ∈ ℤ/ϱℤ, such that a×a−1≡1modϱ, where p ≡ q mod ϱ is the usual modular representation of q ∈ ℤ/ϱℤ. This very special element it is one of the most wideley used mathematical concept in science, engineering and subject areas include the particle physics, the analysis and design of algorithms, data structures, databases, and computer architecture. In this paper, we establish a promising decomposition law for (MMI). In this respect, the main purpose of this paper it is shown that it is possible to express the (MMI) in terms of certain modular multiplicative inverse operators (MMIO) all, well-defined on Group of units pre-established. The main point to note here is that the result of this paper, which expands a result originally presented in [3], does not include any special conditions on the parameters involved.