Article in volume
Authors:
Dimpy Mala Dutta
North-Eastern Hill University, Shillong-793022, India.
email: dimpymdutta@gmail.com
Ardeline Mary Buhphang
North-Eastern Hill University, Shillong-793022, India.
email: ardeline17@gmail.com
Title:
On nil ideals of Leavitt path algebras over commutative rings
PDFSource:
Discussiones Mathematicae - General Algebra and Applications 44(2) (2024) 439-449
Received: 2023-03-08 , Revised: 2023-09-08 , Accepted: 2023-09-08 , Available online: 2024-04-16 , https://doi.org/10.7151/dmgaa.1454
Abstract:
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. We obtain results on the Jacobson radical of L_R(E) for a graph E with no regular vertex. 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 Koethe's conjecture.
Primary keywords:
Leavitt path algebras, Nil ideals, Jacobson radical, arbitrary graph
Secondary keywords:
right quasi-regular, Laurent polynomial, locally nilpotent
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