A generalization of n-ary prime subhypermodule

Let (M, f, g) be an (m, n)-hypermodule over an (m, n)-hyperring (R, h, k). A proper subhypermodule N of M is called n-ary 2-absorbing subhypermodule if whenever g(r₁ⁿ⁻¹, m) ⊆ N for some r₁ⁿ⁻¹ ∈ R and m ∈ M, then either g(r₁ⁿ⁻¹, M) ⊆ N or g(r_i, m, 1_R⁽ⁿ⁻²⁾) ⊆ N for some i ∈ {1, . . ., n − 1}. Various properties of n-ary 2-absorbing subhy-permodules are investigated. In particular, it is shown that if N is a subhypermodule of an (m, n)-hypermodule (M, f, g) over an (m, n)- hyperring (R, h, k), then N is n-ary 2-absorbing if and only if whenever g(I₁, I₂, 1_R⁽ⁿ⁻³⁾, L) ⊆ N for some hyperideals I₁, I₂ of R and subhyper- module L of M, then either g(I₁, I₂, 1_R⁽ⁿ⁻³⁾, M) ⊆ N or g(I₁, 1_R⁽ⁿ⁻²⁾, L) ⊆ N or g(I₂, 1_R⁽ⁿ⁻²⁾, L) ⊆ N. Also, n-ary 2-absorbing subhypermodules in multiplication (m, n)-hypermodules are studied.