Geodesic
On Nil ideals and Jacobson radical of Leavitt path algebras over commutative rings
Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 2, pp. 439-449

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We show in this paper that for any graph E and for a commutative unital ring R, the nil ideals of the Leavitt path algebra L_R(E) depend solely on the nil ideals of the ring R. A connection between the Jacobson radical of L_R(E) and the Jacobson radical of R is obtained. We also prove that for a nil ideal I of a Leavitt path algebra L_R(E) the ideal M_2(I) is also nil, thus obtaining that Leavitt path algebras over arbitrary graphs satisfy the Köethe's conjecture.
Keywords: Leavitt path algebras, Nil ideals, Jacobson radical, arbitrary graph 
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Dutta, Dimpy Mala; Buhphang, Ardeline Mary. On Nil ideals and Jacobson radical of Leavitt path algebras over  commutative rings. Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 2, pp. 439-449. http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a12/