classical prime subhypermodules and related extensions

In this paper, we extend the notion of prime subhypermodules to n-ary classical prime, n-ary weakly classical prime and n-ary ϕ-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. we think the knowledge gained in this setting provides a significant step in the general investigation of subhypermodules