On modules satisfying s-noetherian spectrum condition - KOÇ, SUAT; TEKİR, ÜNSAL (My University, 2022)
Let R be a commutative ring having nonzero identity and M be a unital R-module. Assume that S ⊆ R is a multiplicatively closed subset of R. Then, M satisfies SNoetherian spectrum condition if for each submodule N of M, there exist s ∈ S and a finitely generated submodule F ⊆ N such that sN ⊆ radM (F), where radM (F) is the prime radical of F in the sense (McCasland and Moore in Commun Algebra 19(5):1327–1341, 1991). Besides giving many properties and characterizations of SNoetherian spectrum condition, we prove an analogous result to Cohen’s theorem for modules satisfying S-Noetherian spectrum condition. Moreover, we characterize modules having Noetherian spectrum in terms of modules satisfying the S-Noetherian spectrum condition.
Keywords: Matematik; Değişmeli Halkalar ve Cebirler; Temel Bilimler; Mathematics; Commutative Rings and Algebras; Natural Sciences; Temel Bilimler (SCI); Doğa Bilimleri Genel; ÇOK DİSİPLİNLİ BİLİMLER; MATEMATİK; Natural Sciences (SCI); NATURAL SCIENCES, GENERAL; MATHEMATICS; MULTIDISCIPLINARY SCIENCES; Multidisciplinary; Discrete Mathematics and Combinatorics; Geometry and Topology; Logic; Physical Sciences; Noetherian modules; S-Noetherian modules; Noetherian spectrum; S-Noetherian spectrum condition