On divisor topology of modules over domains
Communications in Algebra, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1080/00927872.2026.2633273
- Dergi Adı: Communications in Algebra
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
- Anahtar Kelimeler: Divisor topology, pseudo-simple module, simple module, uniserial module
- Yıldız Teknik Üniversitesi Adresli: Hayır
Özet
Let M be a module over a domain R and (Formula presented.) be the set of all nonzero nongenerators of M. Consider the following equivalence relation (Formula presented.) on (Formula presented.) given by (Formula presented.) if and only if (Formula presented.) for every (Formula presented.). Let (Formula presented.) be the set of all equivalence classes of (Formula presented.) with respect to (Formula presented.). In this paper, we construct a topology on (Formula presented.) which is called the divisor topology of M and is denoted by (Formula presented.). Actually, (Formula presented.) is an extension of the divisor topology (Formula presented.) over domains to modules in the sense of Yiğit and Koç. We investigate separation axioms (Formula presented.) for every (Formula presented.) first and second countability, connectivity, compactness, nested property, and Noetherian property on (Formula presented.). Also, we characterize some important classes of modules such as uniserial modules, simple modules, vector spaces, and finitely cogenerated modules in terms of (Formula presented.). Furthermore, we prove that (Formula presented.) is a Baire space for factorial modules. Finally, we introduce and study pseudo simple modules which is a new generalization of simple modules, and use them to determine when (Formula presented.) is a discrete space.