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 $\left(m,n\right)$-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.

9 pages, amslatex, the journal version: small corrections and changes, Example 2.1 and Conclusions added, Bibliography updated; https://www.mdpi.com/2073-8994/14/12/2591

References in corpus (3)

• $p$-Adic Mathematical Physics: The First 30 Years
• Polyadic analog of Grothendieck group
• Polyadic integer numbers and finite (m,n)-fields