On s-maximal ideals - TEKİR, ÜNSAL (My University, 2022)
Let R be a commutative ring with nonzero identity and S be a multiplicatively closed subset of R. An ideal P of R that is disjoint from S is called S-maximal ideal if there exists a fixed s ∈ S such that P ⊆ Q for some ideal Q of R implies either sQ ⊆ P or Q ∩ S ̸= ∅. In this study, first we give some relations between S-prime and S-maximal ideals that are generalizations of prime and maximal ideals, respectively. Moreover, we investigate the behaviour of S-maximal ideals under homomorphisms, rings of fractions, in factor rings.
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; Mantık; Geometri ve Topoloji; Ayrık Matematik ve Kombinatorik; Multidisipliner; Fizik Bilimleri; Logic; Geometry and Topology; Discrete Mathematics and Combinatorics; Multidisciplinary; Physical Sciences; magnetic field; electro-osmotic flow; slip velocity; analytical solution