On Quasi Maximal Ideals

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Atıf İçin Kopyala

Alan M., Kılıç M., Koç S., Tekir Ü.

COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES, cilt.76, sa.12, ss.1801-1810, 2023 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 76 Sayı: 12
• Basım Tarihi: 2023
• Doi Numarası: 10.7546/crabs.2023.12.01
• Dergi Adı: COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED)
• Sayfa Sayıları: ss.1801-1810
• Marmara Üniversitesi Adresli: Evet

Özet

Let R be a commutative ring with 1 ̸= 0. A proper ideal I of R is said to

be a quasi maximal ideal if for every a ∈ R − I, either I + Ra = R or I + Ra

is a maximal ideal of R. This class of ideals lies between 2-absorbing ideals

and maximal ideals which is different from prime ideals. In addition to give

fundamental properties of quasi maximal ideals, we characterize principal ideal

UN-rings with √

0

2

= (0), direct product of two fields, and Noetherian zero

dimensional modules in terms of quasi maximal ideals.