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Date Published: 10/10/2020
Online Published: 10/10/2020
Abstract Views: 29
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DOI: https://doi.org/10.52714/dthu.9.5.2020.816
Issue
Vol. 9 No. 5 (2020): Natural Sciences Issue (English)
Section
Natural Sciences Issue
How to Cite
Le, H. M. (2020). The jacobson radical types of Leavitt path algebras with coefficients in a commutative unital semiring. Dong Thap University Journal of Science, 9(5), 42-50. https://doi.org/10.52714/dthu.9.5.2020.816

The jacobson radical types of Leavitt path algebras with coefficients in a commutative unital semiring

Hoang Mai Le1,
1 Department of Mathematics Teacher Education, Dong Thap University, Vietnam

Main Article Content

Abstract

In this paper, we calculate the J - radical and Js - radical of the Leavitt path algebras with coefficients in a commutative semiring of some finite graphs. In particular, we calculate J - radical and Js  - radical of the Leavitt path algebras with coefficients in a field of acyclic graphs, no-exit graphs and give applicable examples.

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Keywords

Acyclic graph, J - radical of semiring, Js - radical of semiring, Leavitt path algebra, no-exit graph

References

Abrams, G. (2015). Leavitt path algebras: the first decade. Bulletin of Mathematical Sciences, (5), 59-120.
Abrams, G., & Pino, G. A. (2005). The Leavitt path algebra of a graph. Journal of Algebra, (293), 319-334.
Bourne, S. (1951). The Jacobson radical of a semiring. Proceedings of the National Academy of Sciences of the United States of America, (37), 163-170.
Golan, J. (1999). Semirings and their Applications. Kluwer Academic Publishers, Dordrecht-Boston-London.
Lizuka, K. (1959). On the Jacobson radical of a semiring. Tohoku Mathematical Journal, (11), 409-421.
Katsov, Y., & Nam, T. G. (2014). On radicals of semirings and ralated problems. Communication Algebra, (42), 5065-5099.
Leavitt, W. G. (1962). The module type of a ring. Transactions of the American Mathematical Society, (103), 113-130.
Katsov, Y., Nam, T. G., & Zumbrägel, J. (2017). Simpleness of Leavitt path algebras with coefficients in a commutative semiring. Semigroup Forum, (94), 481-499.
Mai, L. H., & Tuyen, N. X. (2017). Some remarks on the Jacobson Radical Types of Semirings and Related Problems. Vietnam Journal of Mathematics, (45), 493-506.
Nam, T. G., & Phuc, N. T. (2019). The structure of Leavitt path algebras and the Invariant Basis Number property. Journal of Pure and Applied Algebra, (223), 4827- 4856.
Tomforde, M. (2011). Leavitt path algebras with coefficients in a commutative ring. Journal of Pure and Applied Algebra, (215), 471-484.