Classical prime subhypermodules and related classes

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.