ON QUASI MAXIMAL IDEALS OF COMMUTATIVE RINGS

被引：0

作者：

Alan, Murat ^{[1
]}

Kilic, Mesut ^{[1
]}

Koc, Suat ^{[2
]}

Tekir, Unsal ^{[3
]}

机构：

[1] Yildiz Tech Univ, Dept Math, Davutpasa Campus, TR-34210 Istanbul, Turkiye

[2] Istanbul Medeniyet Univ Uskuddar, Dept Math, TR-34700 Istanbul, Turkiye

[3] Marmara Univ, Dept Math, TR-34722 Ziverbey Istanbul, Turkiye

来源：

COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES | 2023年 / 76卷 / 12期

关键词：

maximal ideal; quasi-maximal ideal; prime ideal; primary ideal; 2-absorbing ideal;

D O I：

10.7546/CRABS.2023.12.01

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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 E 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 V02 = (0), direct product of two fields, and Noetherian zero dimensional modules in terms of quasi maximal ideals.

引用

页码：1801 / 1810

页数：10

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