A generalization of n-ary prime subhypermodule

Abstract

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(ri, m, 1R(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, 1R(n−3), L) ⊆ N for some hyperideals I1, I2 of R and subhyper- module L of M, then either g(I1, I2, 1R(n−3), M) ⊆ N or g(I1, 1R(n−2), L) ⊆ N or g(I2, 1R(n−2), L) ⊆ N. Also, n-ary 2-absorbing subhypermodules in multiplication (m, n)-hypermodules are studied.

Keywords

• (m, n)-hypermodules
• n-ary 2-absorbing subhypermodules
• n-ary prime subhypermodules
• n-ary 2-absorbing hyperideals
• primary secondary