Article
Version 2
Preserved in Portico This version is not peer-reviewed
Polyadic Rings of p-adic Integers
Version 1
: Received: 4 November 2022 / Approved: 10 November 2022 / Online: 10 November 2022 (02:00:13 CET)
Version 2 : Received: 28 November 2022 / Approved: 29 November 2022 / Online: 29 November 2022 (03:39:52 CET)
Version 2 : Received: 28 November 2022 / Approved: 29 November 2022 / Online: 29 November 2022 (03:39:52 CET)
A peer-reviewed article of this Preprint also exists.
Duplij, S. Polyadic Rings of p-Adic Integers. Symmetry 2022, 14, 2591. Duplij, S. Polyadic Rings of p-Adic Integers. Symmetry 2022, 14, 2591.
Abstract
In this note we, first, recall that the sets of all representatives of some special ordinary residue classes become $\left( m,n\right) $-rings. Second, we introduce a possible $p$-adic analog of the residue class modulo a $p$-adic integer. Then, we find the relations which determine, when the representatives form a $\left( m,n\right) $-ring. At the very short spacetime scales such rings could lead to new symmetries of modern particle models.
Keywords
polyadic semigroup; polyadic ring; arity; querelement; residue class; representative; p-adic integer
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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