Prime Ideals in Leibniz Algebras

Document Type

Article

Publication Date

1-1-2024

Publication Title

Journal of Lie Theory

Abstract

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.

Volume Number

34

Issue Number

1

First Page

41

Last Page

49

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