Multiplication modules with prime spectrum
TURKISH JOURNAL OF MATHEMATICS, cilt.43, sa.4, ss.2000-2009, 2019 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 43 Sayı: 4
- Basım Tarihi: 2019
- Doi Numarası: 10.3906/mat-1803-54
- Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.2000-2009
- Anahtar Kelimeler: Multiplication module, prime submodule, spectrum of module
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Akdeniz Üniversitesi Adresli: Evet
Özet
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.