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

Yıl 2023, Cilt: 33 Sayı: 33, 34 - 53, 09.01.2023
https://doi.org/10.24330/ieja.1229771

Öz

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.

Kaynakça

  • 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.
Yıl 2023, Cilt: 33 Sayı: 33, 34 - 53, 09.01.2023
https://doi.org/10.24330/ieja.1229771

Öz

Kaynakça

  • 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.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Trinh Thanh DEO Bu kişi benim

Vo Thanh CHI Bu kişi benim

Yayımlanma Tarihi 9 Ocak 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 33 Sayı: 33

Kaynak Göster

APA DEO, T. T., & CHI, 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, CHI VT. On some ideal structure of Leavitt path algebras with coefficients in integral domains. IEJA. Ocak 2023;33(33):34-53. doi:10.24330/ieja.1229771
Chicago DEO, Trinh Thanh, ve Vo Thanh CHI. “On Some Ideal Structure of Leavitt Path Algebras With Coefficients in Integral Domains”. International Electronic Journal of Algebra 33, sy. 33 (Ocak 2023): 34-53. https://doi.org/10.24330/ieja.1229771.
EndNote DEO TT, CHI VT (01 Ocak 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 ve V. T. CHI, “On some ideal structure of Leavitt path algebras with coefficients in integral domains”, IEJA, c. 33, sy. 33, ss. 34–53, 2023, doi: 10.24330/ieja.1229771.
ISNAD DEO, Trinh Thanh - CHI, Vo Thanh. “On Some Ideal Structure of Leavitt Path Algebras With Coefficients in Integral Domains”. International Electronic Journal of Algebra 33/33 (Ocak 2023), 34-53. https://doi.org/10.24330/ieja.1229771.
JAMA DEO TT, CHI VT. On some ideal structure of Leavitt path algebras with coefficients in integral domains. IEJA. 2023;33:34–53.
MLA DEO, Trinh Thanh ve Vo Thanh CHI. “On Some Ideal Structure of Leavitt Path Algebras With Coefficients in Integral Domains”. International Electronic Journal of Algebra, c. 33, sy. 33, 2023, ss. 34-53, doi:10.24330/ieja.1229771.
Vancouver DEO TT, CHI VT. On some ideal structure of Leavitt path algebras with coefficients in integral domains. IEJA. 2023;33(33):34-53.