Polyadic Rings of p-Adic Integers

Abstract

In this note, we first recall that the sets of all representatives of some special ordinary residue classes become m,n-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 m,n-ring. At very short spacetime scales, such rings could lead to new symmetries of modern particle models.