e-Idempotent Matrices over Commutative Semirings
Main Article Content
Abstract
In this work, we introduce the notion of -idempotent matrices over a commutative semiring, this is a generalization of the idempotent matrices. We investigate some characteristic properties of -idempotent matrices over general semirings. We provide a formula to calculate the number of -idempotent triangular matrices over finite commutative semirings without zero divisors.
Keywords:
: Semiring, -idempotent matrix, Triangular matrix, Idempotent matrix, -invertible matrix.
References
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[2] K. T. Kang, S. Z. Song, Y. O. Yang, Structures of Idempotent Matrices over Chain Semirings, Bull. Korean Math. Soc., Vol. 44, No. 4, 2007, pp. 721-729, https//doi.org/10.4134/BKMS.2007.44.4.721.
[3] L. B. Beasley, A. E. Guterman, K. T. Kang, S. Z. Song, Idempotent Boolean Matrices and Majorization, J. Math. Sci., Vol. 152, No. 4, 2008, pp. 456-468, https//doi.org/10.1007/s10958-008-9086-3.
[4] D. Dolžan, P. Oblak, Idempotent Matrices over Antirings, Linear Algebra Appl., Vol. 431, No. 5-7, 2009,
pp. 823-832, https//doi.org/10.1016/j.laa.2009.03.035.
[5] H. C. Cong, Idempotent Triangular Matrices over Commutative Semirings, TNU J. Sci. Technol., Vol. 229,
No. 06, 2024, pp. 57-64, https//doi.org/10.34238/tnu-jst.8971.
[6] J. S. Golan, Semirings and Their Applications. Kluwer Academic Publishers, Dordrecht-Boston-London, 1999.
[7] Y. J. Tan, Diagonability of Matrices over Commutative Semirings, Linear Multilinear Algebr., Vol. 68, No. 9, 2020, pp. 1743-1752, https//doi.org/10.1080/03081087.2018.1556243.
[8] L. Zhang, Y. Shao, E-invertible Matrices over Commutative Semirings, Indian J. Pure Appl. Math., Vol. 49,
No. 2, 2018, pp. 227-238, https//doi.org/10.1007/s13226-018-0265-8.