Prime Ideals in Leibniz Algebras

被引：0
|
作者：
Biyogmam, Guy R. [1 ]
Safa, Hesam [2 ]
机构：
[1] Georgia Coll & State Univ, Dept Math, Milledgeville, GA USA
[2] Univ Bojnord, Fac Basic Sci, Dept Math, Bojnurd, Iran
来源：
JOURNAL OF LIE THEORY | 2024年 / 34卷 / 01期
关键词：
Leibniz algebra; Leibniz kernel; prime ideal; semi-prime ideal;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The notions of prime and semi -prime ideals of Leibniz algebras are introduced and the interrelation of these notions with maximal ideals, irreducible ideals and solvable radical are investigated. We prove that a maximal ideal of a Leibniz algebra is prime if and only if its codimension is greater than one. Also, it is shown that if a Leibniz algebra g satisfies the maximal condition on ideals, then the intersection of all prime ideals, the intersection of all semi -prime ideals, and the solvable radical of g are all equal.
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页码：41 / 49
页数：9
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