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, Tome 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.
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, Tome 34 (2024) no. 1, pp. 41-49. http://geodesic.mathdoc.fr/item/JOLT_2024_34_1_a2/
@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},
url = {http://geodesic.mathdoc.fr/item/JOLT_2024_34_1_a2/}
}
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AU - Hesam Safa
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