Araştırma Makalesi

Yıl 2023,
Cilt: 33 Sayı: 33, 34 - 53, 09.01.2023
### Öz

### Anahtar Kelimeler

### Kaynakça

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.

- 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
### Öz

### Anahtar Kelimeler

### 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.

Birincil Dil | İngilizce |
---|---|

Konular | Matematik |

Bölüm | Makaleler |

Yazarlar | |

Yayımlanma Tarihi | 9 Ocak 2023 |

Yayımlandığı Sayı | Yıl 2023 Cilt: 33 Sayı: 33 |