On quasi maximal ideals - TEKİR, ÜNSAL (My University, 2023)
Let R be a commutative ring with 1 ̸= 0. A proper ideal I of R is said tobe a quasi maximal ideal if for every a ∈ R − I, either I + Ra = R or I + Rais a maximal ideal of R. This class of ideals lies between 2-absorbing idealsand maximal ideals which is different from prime ideals. In addition to givefundamental properties of quasi maximal ideals, we characterize principal idealUN-rings with √02= (0), direct product of two fields, and Noetherian zerodimensional modules in terms of quasi maximal ideals.
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