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On some ideal structure of Leavitt path algebras with coefficients in integral domains

Year 2023, Volume: 33 Issue: 33, 34 - 53, 09.01.2023

Trinh Thanh Deo Vo Thanh Chı

https://doi.org/10.24330/ieja.1229771
Cited By: 1

Abstract

In this paper, we present results concerning the structure of the ideals in the Leavitt path algebra of a (countable) directed graph with coefficients in an integral domain, such as, describing the set of generators for an ideal; the necessary and sufficient conditions for an ideal to be prime; the necessary and sufficient conditions for a Leavitt path algebra to be simple. Besides, some other interesting properties of ideal structure in a Leavitt path algebra are also mentioned.

Keywords

Leavitt path algebra prime ideal basic ideal maximal ideal

References

  • G. Abrams, P. Ara and M. S. Molina, Leavitt Path Algebras, Lect. Notes in Math., 2191, Springer, London, 2017.
  • G. Abrams, J. P. Bell, P. Colak and K. M. Rangaswamy, Two-sided chain conditions in Leavitt path algebras over arbitrary graphs, J. Algebra Appl., 11(3) (2012), 1250044 (23 pp.).
  • S. Esin and M. Kanuni Er, Existence of maximal ideals in Leavitt path algebras, Turkish J. Math., 42 (2018), 2081-2090.
  • P. Kanwar, M. Khatkar and R. K. Sharma, On Leavitt path algebras over commutative rings, Int. Electron. J. Algebra, 26 (2019), 191-203.
  • T. Y. Lam, A First Course in Noncommutative Rings, Graduate Texts in Mathematics, Springer-Verlag, New York, 1991.
  • H. Larki, Ideal structure of Leavitt path algebras with coefficients in a unital commutative ring, Comm. Algebra, (43)12 (2015), 5031-5058.
  • M. Mignotte and D. Stefanescu, Polynomials: An Algorithmic Approach, Springer-Verlag, Singapore, 1999.
  • K. M. Rangaswamy, The theory of prime ideals of Leavitt path algebras over arbitrary graphs, J. Algebra, 375 (2013), 73-90.
  • K. M. Rangaswamy, On generator of two-sided ideals of Leavitt path algebras over arbitrary graphs, Comm. Algebra, 42 (2014), 2859-2868.
  • M. Tomforde, Leavitt path algebras with coefficients in a commutative ring, J. Pure Appl. Algebra, 215 (2011), 471-484.

Year 2023, Volume: 33 Issue: 33, 34 - 53, 09.01.2023

Trinh Thanh Deo Vo Thanh Chı

https://doi.org/10.24330/ieja.1229771
Cited By: 1

Abstract

Keywords

Leavitt path algebra prime ideal basic ideal maximal ideal

References

  • G. Abrams, P. Ara and M. S. Molina, Leavitt Path Algebras, Lect. Notes in Math., 2191, Springer, London, 2017.
  • G. Abrams, J. P. Bell, P. Colak and K. M. Rangaswamy, Two-sided chain conditions in Leavitt path algebras over arbitrary graphs, J. Algebra Appl., 11(3) (2012), 1250044 (23 pp.).
  • S. Esin and M. Kanuni Er, Existence of maximal ideals in Leavitt path algebras, Turkish J. Math., 42 (2018), 2081-2090.
  • P. Kanwar, M. Khatkar and R. K. Sharma, On Leavitt path algebras over commutative rings, Int. Electron. J. Algebra, 26 (2019), 191-203.
  • T. Y. Lam, A First Course in Noncommutative Rings, Graduate Texts in Mathematics, Springer-Verlag, New York, 1991.
  • H. Larki, Ideal structure of Leavitt path algebras with coefficients in a unital commutative ring, Comm. Algebra, (43)12 (2015), 5031-5058.
  • M. Mignotte and D. Stefanescu, Polynomials: An Algorithmic Approach, Springer-Verlag, Singapore, 1999.
  • K. M. Rangaswamy, The theory of prime ideals of Leavitt path algebras over arbitrary graphs, J. Algebra, 375 (2013), 73-90.
  • K. M. Rangaswamy, On generator of two-sided ideals of Leavitt path algebras over arbitrary graphs, Comm. Algebra, 42 (2014), 2859-2868.
  • M. Tomforde, Leavitt path algebras with coefficients in a commutative ring, J. Pure Appl. Algebra, 215 (2011), 471-484.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Trinh Thanh Deo This is me

Vo Thanh Chı This is me

Publication Date January 9, 2023
Published in Issue Year 2023 Volume: 33 Issue: 33

Cite

APA Deo, T. T., & Chı, V. T. (2023). On some ideal structure of Leavitt path algebras with coefficients in integral domains. International Electronic Journal of Algebra, 33(33), 34-53. https://doi.org/10.24330/ieja.1229771
AMA Deo TT, Chı VT. On some ideal structure of Leavitt path algebras with coefficients in integral domains. IEJA. January 2023;33(33):34-53. doi:10.24330/ieja.1229771
Chicago Deo, Trinh Thanh, and Vo Thanh Chı. “On Some Ideal Structure of Leavitt Path Algebras With Coefficients in Integral Domains”. International Electronic Journal of Algebra 33, no. 33 (January 2023): 34-53. https://doi.org/10.24330/ieja.1229771.
EndNote Deo TT, Chı VT (January 1, 2023) On some ideal structure of Leavitt path algebras with coefficients in integral domains. International Electronic Journal of Algebra 33 33 34–53.
IEEE T. T. Deo and V. T. Chı, “On some ideal structure of Leavitt path algebras with coefficients in integral domains”, IEJA, vol. 33, no. 33, pp. 34–53, 2023, doi: 10.24330/ieja.1229771.
ISNAD Deo, Trinh Thanh - Chı, Vo Thanh. “On Some Ideal Structure of Leavitt Path Algebras With Coefficients in Integral Domains”. International Electronic Journal of Algebra 33/33 (January 2023), 34-53. https://doi.org/10.24330/ieja.1229771.
JAMA Deo TT, Chı VT. On some ideal structure of Leavitt path algebras with coefficients in integral domains. IEJA. 2023;33:34–53.
MLA Deo, Trinh Thanh and Vo Thanh Chı. “On Some Ideal Structure of Leavitt Path Algebras With Coefficients in Integral Domains”. International Electronic Journal of Algebra, vol. 33, no. 33, 2023, pp. 34-53, doi:10.24330/ieja.1229771.
Vancouver Deo TT, Chı VT. On some ideal structure of Leavitt path algebras with coefficients in integral domains. IEJA. 2023;33(33):34-53.

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