On characterization of tripotent matrices in triangular matrix rings
Yıl: 2021 Cilt: 45 Sayı: 5 Sayfa Aralığı: 1914 - 1926 Metin Dili: İngilizce DOI: 10.3906/mat-2103-109 İndeks Tarihi: 01-07-2022
On characterization of tripotent matrices in triangular matrix rings
Öz: Let R be a ring with identity 1 whose tripotents are only −1, 0, and 1. It is characterized the structure
of tripotents in T (R) which is the ring of triangular matrices over R. In addition, when R is finite, it is given number
of the tripotents in Tn(R) which is the ring of n × n dimensional triangular matrices over R with n being a positive
integer.
Anahtar Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
- [1] Baksalary JK, Baksalary OM. Idempotency of linear combinations of two idempotent matrices. Linear Algebra and its Applications 2000; 321: 3-7.
- [2] Baksalary JK, Baksalary OM, Styan GPH. Idempotency of linear combinations of an idempotent matrix and a tripotent matrix. Linear Algebra and its Applications 2002; 354: 21-34.
- [3] Baksalary JK, Baksalary OM, Özdemir H. A note on linear combinations of commuting tripotent matrices. Linear Algebra and its Applications 2004; 388: 45-51.
- [4] Baksalary OM. On idempotency of linear combinations of three idempotent matrix, two of which are disjoint. Linear Algebra and its Applications 2004; 388: 67-68.
- [5] Baksalary OM, Benítez J. Idempotency of linear combinations of three idempotent matrix, two of which are commuting. Linear Algebra and its Applications 2007; 424: 320-337.
- [6] Benítez J, Thome N. Idempotency of linear combinations of an idempotent matrix and a t-potent matrix that commute. Linear Algebra and its Applications 2005; 403: 414-418.
- [7] Benítez, J, Zhang M, Liu X. Involutiveness of linear combinations of a quadratic or tripotent matrix and an arbitrary matrix. Bulletin of the Iranian Mathematical Society 2016; 42 (3): 595-610.
- [8] Chen J, Wang Z, Zhou Y. Rings in which elements are uniquely the sum of an idempotent and a unit that commute. Journal of Pure Applied Algebra 2009; 213: 215-223.
- [9] Cheraghpour H, Ghosseiri Nader M. On the idempotents, nilpotents, units and zero-divisors of finite rings. Linear and Multilinear Algebra 2019; 67 (2): 327-336.
- [10] Chuang X, Runzhang X. Tripotency of a linear combination of two involutory matrices and a tripotent matrix that mutually commute. Linear Algebra and its Applications 2012; 437 (9): 2091-2109.
- [11] Danchev PV. Rings whose elements are sums of three or minus sums of two commuting idempotents. Albanian Journal of Mathematics 2018; 12 (1): 3-7.
- [12] De Seguins Pazzis C. On sums of idempotent matrices over a field of positive characteristic. Linear Algebra and its Applications 2010; 433 (4): 856-866.
- [13] Graybill FA. Matrices with Applications in Statistics. Belmont, CA, USA: Wadsworth International Group, 1983.
- [14] Hirano Y, Tominaga H. Rings in which every element is the sum of two idempotents. Bulletin of Australian Mathematical Society 1988; 37 (2): 161-164.
- [15] Hou X. Idempotents in triangular matrix rings. Linear and Multilinear Algebra 2021; 69 (2): 296-304. doi: 10.1080/03081087.2019.1596223
- [16] Özdemir H, Özban AY. On idempotency of linear combinations of an idempotent matrix. Applied Mathematics and Computation 2004; 159: 439-448.
- [17] Özdemir H, Sarduvan M, Özban AY, Güler N. On idempotency and tripotency of linear combinations of two commuting tripotent matrices. Applied Mathematics and Computations 2009; 207: 197-201.
- [18] Petik T, Uc̣ M, Özdemir H. Generalized quadraticity of linear combination of two generalized quadratic matrices. Linear and Multilinear Algebra 2015; 63 (12): 2430-2439.
- [19] Petik T, Gökmen BT. Alternative characterizations of some linear combinations of an idempotent matrix and a tripotent matrix that commute. Journal of Balıkesir University Institute of Science and Technology 2020; 22 (1): 255-268.
- [20] Petik T, Hocaoǧlu L, Özdemir H. Involutives in triangular matrix rings. Bilecik Şeyh Edebali University Journal of Science 2020; 7 (1): 91-103.
- [21] Sarduvan M, Kalaycı N. On idempotency of linear combinations of a quadratic or a cubic matrix and an arbitrary matrix. Filomat 2019; 33 (10): 3161-3185.
- [22] Sheibani M, Huanyin C. Rings over which every matrix is the sum of a tripotent and a nilpotent. arXiv 2017; arXiv:1702.05605v1.
- [23] Uc̣ M, Petik T, Özdemir H. The generalized quadraticity of linear combinations of two commuting quadratic matrices. Linear and Multilinear Algebra 2016; 64 (9): 1696-1715.
- [24] Tang G, Zhou Y, Su H. Matrices over a commutative ring as sums of three idempotents or three involutions. Linear and Multilinear Algebra 2019; 67 (2): 267-277.
- [25] Wu Y. K-Potent matrices-construction and applications in digital image encryption. In: Recent Advances in Applied Mathematics, AMERICAN-MATH’10: Proceedings of the 2010 American Conference on Applied mathematics; Cambridge, MA, USA; 2010. pp. 455-460.
- [26] Wright SE. Triangular idempotent matrices over a general ring. Linear and Multilinear Algebra 2020. doi: 10.1080/03081087.2020.1773377
- [27] Ying Z, Koṣan T, Zhou Y. Rings in which every element is a sum of two tripotents. Canadian Mathematical Bulletin 2016; 59 (3): 661-672.
- [28] Zhou Y. Rings in which elements are sums of nilpotents, idempotents and tripotents. Journal of Algebra and its Applications 2018; 17 (1): 1850009.
APA | Demirkol T (2021). On characterization of tripotent matrices in triangular matrix rings. , 1914 - 1926. 10.3906/mat-2103-109 |
Chicago | Demirkol Tuğba On characterization of tripotent matrices in triangular matrix rings. (2021): 1914 - 1926. 10.3906/mat-2103-109 |
MLA | Demirkol Tuğba On characterization of tripotent matrices in triangular matrix rings. , 2021, ss.1914 - 1926. 10.3906/mat-2103-109 |
AMA | Demirkol T On characterization of tripotent matrices in triangular matrix rings. . 2021; 1914 - 1926. 10.3906/mat-2103-109 |
Vancouver | Demirkol T On characterization of tripotent matrices in triangular matrix rings. . 2021; 1914 - 1926. 10.3906/mat-2103-109 |
IEEE | Demirkol T "On characterization of tripotent matrices in triangular matrix rings." , ss.1914 - 1926, 2021. 10.3906/mat-2103-109 |
ISNAD | Demirkol, Tuğba. "On characterization of tripotent matrices in triangular matrix rings". (2021), 1914-1926. https://doi.org/10.3906/mat-2103-109 |
APA | Demirkol T (2021). On characterization of tripotent matrices in triangular matrix rings. Turkish Journal of Mathematics, 45(5), 1914 - 1926. 10.3906/mat-2103-109 |
Chicago | Demirkol Tuğba On characterization of tripotent matrices in triangular matrix rings. Turkish Journal of Mathematics 45, no.5 (2021): 1914 - 1926. 10.3906/mat-2103-109 |
MLA | Demirkol Tuğba On characterization of tripotent matrices in triangular matrix rings. Turkish Journal of Mathematics, vol.45, no.5, 2021, ss.1914 - 1926. 10.3906/mat-2103-109 |
AMA | Demirkol T On characterization of tripotent matrices in triangular matrix rings. Turkish Journal of Mathematics. 2021; 45(5): 1914 - 1926. 10.3906/mat-2103-109 |
Vancouver | Demirkol T On characterization of tripotent matrices in triangular matrix rings. Turkish Journal of Mathematics. 2021; 45(5): 1914 - 1926. 10.3906/mat-2103-109 |
IEEE | Demirkol T "On characterization of tripotent matrices in triangular matrix rings." Turkish Journal of Mathematics, 45, ss.1914 - 1926, 2021. 10.3906/mat-2103-109 |
ISNAD | Demirkol, Tuğba. "On characterization of tripotent matrices in triangular matrix rings". Turkish Journal of Mathematics 45/5 (2021), 1914-1926. https://doi.org/10.3906/mat-2103-109 |