DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score: 0.4

SJR: 0.203

SNIP: 0.562

MCQ: 0.12

Index Copernicus: 121.02

Discussiones Mathematicae - General Algebra and Applications

Article in press

Authors:

D.M. Dutta

Dimpy Mala Dutta

North-Eastern Hill University, Shillong-793022, India.

email: dimpymdutta@gmail.com

A.M. Buhphang

Ardeline Mary Buhphang

North-Eastern Hill University, Shillong-793022, India.

email: ardeline17@gmail.com

0000-0003-3795-7140

Title:

On nil ideals of Leavitt path algebras over commutative rings

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Source:

Discussiones Mathematicae - General Algebra and Applications

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

References:

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