On some specific results of rings with prime nilradical

被引：0
|
作者：
Alhazmy, Khaled [1 ]
Almahdi, Fuad Ali Ahmed [1 ]
El Haddaoui, Younes [2 ]
Mahdou, Najib [2 ]
机构：
[1] King Khalid Univ, Fac Sci, Dept Math, POB 9004, Abha, Saudi Arabia
[2] Univ SM Ben Abdellah, Fac Sci & Technol Fez, Dept Math, Modelling & Math Struct Lab, Fes, Morocco
来源：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2025年 / 24卷 / 06期
关键词：
N-prime ideals; nonnil-primary ideals; nonnil-Noetherian modules; associated prime ideals; phi-chained rings; phi-Prufer rings;
D O I：
10.1142/S021949882550152X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The authors of A. Benhissi and S. Hizem [Nonnil-Noetherian rings and SFT property, Rocky Mountain J. Math. 41 (2011) 1483-1500] proved that the primary decomposition of a nonnil-ideal of a nonnil-Noetherian ring always exists. We will show in this paper that this primary decomposition is minimal. We next prove that over any nonnil-Noetherian ring, a sub-class of modules admit a primary decomposition. In the second part of this paper, we give some properties related to phi-chained and phi-Prufer rings.
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页数：25
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