TURKISH JOURNAL OF MATHEMATICS, vol.43, no.4, pp.2000-2009, 2019 (SCI-Expanded)
Article / Article
TURKISH JOURNAL OF MATHEMATICS
Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
Multiplication module, prime submodule, spectrum of module
Akdeniz University Affiliated:
The subject of this paper is the Zariski topology on a multiplication module M over a commutative ring R. We find a characterization for the radical submodule rad(M)(0) and also show that there are proper ideals I-1, ..., I-n of R such that rad(M)(0) = rad(M)((I-1...I-n) M) . Finally, we prove that the spectrum Spec(M) is irreducible if and only if M is the finite sum of its submodules, whose tau-radicals are prime in M.