Multiplication $(m,n)$-hypermodules

TL;DR

This paper explores the properties and structure of multiplication $(m,n)$-hypermodules over commutative Krasner $(m,n)$-hyperrings, extending the theoretical framework of hypermodule theory.

Contribution

It provides an extensive investigation into multiplication $(m,n)$-hypermodules, defining their structure and establishing foundational properties in the context of hyperring modules.

Findings

Characterization of multiplication $(m,n)$-hypermodules

Conditions for subhypermodules to be generated by hyperideals

Extension of hypermodule theory to Krasner hyperrings

Abstract

The concept of multiplication $(m,n)$-hypermodules was introduced by Ameri and Norouzi in \cite{sorc2}. Here we intend to investigate extensively the multiplication $(m,n)$-hypermodules. Let $(M,f,g)$ be a $(m,n)$-hypermodule (with canonical $(m,n)$-hypergroups) over a commutative Krasner $(m,n)$-hyperring $(R,h,k)$. A $(m, n)$-hypermodule $(M, f, g)$ over $(R, h, k)$ is called a multiplication $(m, n)$-hypermodule if for each subhypermodule $N$ of $M$, there exists a hyperideal $I$ of $R$ such that $N =g(I, 1^{(n-2)}, M)$.