
Journal of Lie Theory 34 (2024), No. 1, 041049 Copyright Heldermann Verlag 2024 Prime Ideals in Leibniz Algebras Guy R. Biyogmam Department of Mathematics, Georgia College & State University, Milledgeville, U.S.A. guy.biyogmam@gcsu.edu Hesam Safa Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Iran h.safa@ub.ac.ir The notions of prime and semiprime 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 semiprime ideals, and the solvable radical of g are all equal. Keywords: Leibniz algebra, Leibniz kernel, prime ideal, semiprime ideal. MSC: 17A32, 17A60. [ Fulltextpdf (112 KB)] for subscribers only. 