Publication: On quasi maximal ideals
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Abstract
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.
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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
Citation
Alan M., Kılıç M., Koç S., Tekir Ü., "On Quasi Maximal Ideals", COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES, cilt.76, sa.12, ss.1801-1810, 2023