MMN-358
2-absorbing and $n$-weakly prime submodules
S. Moradi; A. Azizi;Abstract
Let R be a commutative ring with identity, and n > 1 an integer. A
proper submodule N of an R-module M will be called 2-absorbing [resp. n-weakly
prime], if r, s 2 R and x 2 M with rsx 2 N [resp. rsx 2 N (N : M)n−1N] implies
that rs 2 (N : M) or rx 2 N or sx 2 N. These concepts are generalizations of the
notions of 2-absorbing ideals and weakly prime submodules, which have been studied
in [4, 5, 7, 8]. We will study 2-absorbing and n-weakly prime submodules, in this
paper. Among other results, it is proved that if (N : M)n−1N 6= (N : M)2N, then N
is 2-absorbing if and only if it is n-weakly prime.
Vol. 13 (2012), No. 1, pp. 75-86