One-sided nilpotent semicommutative properties of rings

被引：0
|
作者：
He, Ping [1 ]
Zhao, Liang [1 ]
机构：
[1] Anhui Univ Technol, Sch Math & Phys, Maanshan 243032, Peoples R China
来源：
ASIAN-EUROPEAN JOURNAL OF MATHEMATICS | 2024年 / 17卷 / 01期
基金：
美国国家科学基金会;
关键词：
Semicommutative ring; nil-semicommutative ring; semiprime ring; left nilpotent semicommutative ring; ARMENDARIZ RINGS; EXTENSIONS;
D O I：
10.1142/S1793557123502443
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the semicommutative properties of rings with one-sided nilpotent structures. The concepts of left and right nilpotent semicommutative rings are defined and studied, which are a generalization of semicommutative rings. We show that the class of one-sided nilpotent semicommutative rings is strictly placed between the class of semicommutative rings and that of nil-semicommutative rings. As applications, we give some characterizations of semiprime rings from the point of view of left nilpotent semicommutative rings.
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页数：14
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