Hyperoperations in exponential fields

TL;DR

This paper introduces new hyperoperation sequences in exponential fields, analyzing their algebraic structures and constructing related fields through inverse completion, expanding understanding of hyperoperations in algebraic systems.

Contribution

It presents novel hyperoperation sequences, characterizes their algebraic properties, and constructs associated fields, advancing the theoretical framework of hyperoperations in exponential algebra.

Findings

Hyperoperation sequences form monoids and semirings.

Construction of fields via inverse completion from hyperoperations.

Enhanced understanding of algebraic structures in exponential fields.

Abstract

New sequences of hyperoperations \cite{BE15,HI26,ACK28,GO47,TAR69} are presented together with their local algebraic properties. The commutative hyperoperations reported by Bennet \cite{BE15} are presented as a sequence of monoids. After identifying the semirings along the sequence, the corresponding fields are constructed via inverse completion.