Journal of Lie Theory

no. 1
Prime Ideals in Leibniz Algebras
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 
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     author = {G. R. Biyogmam and H. 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/}
}
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G. R. Biyogmam; H. Safa. Prime Ideals in Leibniz Algebras. Journal of Lie Theory, Volume 34 (2024) no. 1, pp. 41-49. doi: 10.5802/jolt.1326

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