Classical prime subhypermodules and related classes

TL;DR

This paper extends the concept of prime subhypermodules to various n-ary classical prime structures within hypermodules over hyperrings, exploring their properties and behavior under different algebraic operations.

Contribution

It introduces new n-ary classical prime subhypermodules and studies their properties, characterizations, and behavior under homomorphisms, quotients, and products.

Findings

Defined n-ary classical prime subhypermodules and related classes

Established properties and characterizations of these structures

Analyzed their behavior under hypermodule homomorphisms, quotients, and products

Abstract

In this paper, we extend the notion of prime subhypermodules to n-ary classical prime, n-ary weakly classical prime and n-ary phi-classical prime subhypermodules of an (m,n)-hypermodule over a commutative Krasner (m,n)-hyperring. Many properties and characterizations of them are introduced. Moreover, we investigate the behavior of these structures under hypermodule homomorphisms, quotient hypermodules and cartesian product.