S-VERSIONS AND S-GENERALIZATIONS OF IDEMPOTENTS, PURE IDEALS AND STONE TYPE THEOREMS
Bulletin of the Korean Mathematical Society, cilt.61, sa.1, ss.83-92, 2024 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 61 Sayı: 1
- Basım Tarihi: 2024
- Doi Numarası: 10.4134/bkms.b230023
- Dergi Adı: Bulletin of the Korean Mathematical Society
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
- Sayfa Sayıları: ss.83-92
- Anahtar Kelimeler: Prime spectrum, pure ideal, S-idempotent, S-Zariski topology, Stone type theorem, Zariski topology
- Yıldız Teknik Üniversitesi Adresli: Evet
Özet
Let R be a commutative ring with nonzero identity and M be an R-module. In this paper, we first introduce the concept of S-idempotent element of R. Then we give a relation between S-idempotents of R and clopen sets of S-Zariski topology. After that we define S-pure ideal which is a generalization of the notion of pure ideal. In fact, every pure ideal is S-pure but the converse may not be true. Afterwards, we show that there is a relation between S-pure ideals of R and closed sets of S-Zariski topology that are stable under generalization.