Journal of Lie Theory

no. 1
Prime Ideals in Leibniz Algebras
Guy R. Biyogmam1; Hesam Safa2
1Department of Mathematics, Georgia College & State University, Milledgeville, U.S.A.
2Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Iran
Journal of Lie Theory, Volume 34 (2024) no. 1, pp. 41-49
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.
DOI: 10.5802/jolt.1326
Classification: 17A32, 17A60
Keywords: Leibniz algebra, Leibniz kernel, prime ideal, semi-prime ideal

Guy R. Biyogmam  1 ; Hesam Safa  2

1 Department of Mathematics, Georgia College & State University, Milledgeville, U.S.A.
2 Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Iran 
Guy R. Biyogmam; Hesam Safa. Prime Ideals in Leibniz Algebras. Journal of Lie Theory, Volume 34 (2024) no. 1, pp. 41-49. doi: 10.5802/jolt.1326
@article{JOLT_2024_34_1_a2,
     author = {Guy R. Biyogmam and Hesam Safa},
     title = {Prime {Ideals} in {Leibniz} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {41--49},
     year = {2024},
     volume = {34},
     number = {1},
     doi = {10.5802/jolt.1326},
     zbl = {1556.17002},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1326/}
}
TY  - JOUR
AU  - Guy R. Biyogmam
AU  - Hesam Safa
TI  - Prime Ideals in Leibniz Algebras
JO  - Journal of Lie Theory
PY  - 2024
SP  - 41
EP  - 49
VL  - 34
IS  - 1
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1326/
DO  - 10.5802/jolt.1326
ID  - JOLT_2024_34_1_a2
ER  - 
%0 Journal Article
%A Guy R. Biyogmam
%A Hesam Safa
%T Prime Ideals in Leibniz Algebras
%J Journal of Lie Theory
%D 2024
%P 41-49
%V 34
%N 1
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.1326/
%R 10.5802/jolt.1326
%F JOLT_2024_34_1_a2

Cited by Sources: