Hypervaluations on ternary semihyperrings

Abstract

This article aims to present the concept of hypervaluation on a commutative ternary semihyperring mapped onto an ordered abelian group. It examines various properties of hyperideals within the ternary semihyperring that correspond to the valuation map. Additionally, the article explores results which are similar to those found in classical valuation rings, but within the framework of hypervalued ternary semihyperrings.