A NOTE ON WEAKLY N-SUBMODULES

Let M be a nonzero unital module over a commutative ring R with a nonzero identity. A proper submodule N of M is said to be a weakly n-submodule if whenever 0 ≠ am ∈ N for some a ∈ R and m ∈ M, then a ∈√ann(M) or m ∈ N. We examine the relations between weakly n-submodules and classical submodules such as prime, weakly prime, weakly primary and r-submodules. Also, we characterize modules over which every nonzero submodule is secondary by using weakly n-submodules. © Palestine Polytechnic University-PPU 2025.