Journal of Lie Theory 34 (2024), No. 1, 041--049
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 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.
Keywords: Leibniz algebra, Leibniz kernel, prime ideal, semi-prime ideal.
MSC: 17A32, 17A60.
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