Strongly irreducible submodules in Noetherian modulesR. Naghipour, M. SedghinLet R denote a commutative Noetherian ring and let M be a finitely generated R-module. The main purpose of this paper is to show that a submodule N of M is strongly irreducible if and only if N is primary of the form (pM)(n) and Mp is arithmetical, where p = Rad(N:RM) and n>1 is an integer. As a consequence we deduce that if R is integral domain and M is torsion-free, then there exists a strongly irreducible submodule N of M such that N:RM is not prime ideal if and only if there is a prime ideal p of R with pM ⊈ N and Mp is an arithmetical Rp-module. These generalize and recover the corrected version of the main results of Heinzer et al. (see [6, Theorem 3.6]) and Khaksari et al. (see [7, Theorem 3.10]).Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 18(2) (2025), pp. 211-222 |