n-pure submodules of modules

چکیده مقاله

let r be a commutative ring, m an r-module, and n ≥ 1 an integer. in this paper, we introduce the concept of n-pure submodules of m as a generalization of pure submodules and obtain some related results. we say that a submodule n of m is a n-pure submodule of m if i1i2...inn = i1n ∩ i2n ∩ ...inn ∩ (i1i2...in)m for all proper ideals i1, i2, ...in of r.