A characterization of clean matrices in M3(Z)


Benchawan Sookcharoenpinyo


    An n x n matrix over a commutative ring with identity is clean if it is the sum of an idempotent matrix and a unit. In 2009, Rajeswari and Aziz gave necessary and sufficient criteria for a matrix in M3(Z) to be clean and discussed the involved Diophantine equations. In this paper, we extend those results to a larger set, M3(Z). We characterize when a matrix  

is clean. As its application, we discuss the relation between clean matrices and the existence of non-trivial solution of certain types of Diophantine equations.


Chen, H. (2009). Clean matrices over commutative rings. Czechoslovak Mathematical Journal, 59(134), 145-158.

Khurana, D. & Lam, T. Y. (2004). Clean matrices and unit-regular matrices. Journal of Algebra, 280, 683-698.

Rajeswari, K. N. & Aziz, R. (2009). A note on clean matrices in . International Journal of Algebra, 3(5), 241- 248.

clean matrix, idempotent matrix, Diophantine equation
Research Articles


How to Cite
SOOKCHAROENPINYO, Benchawan. A characterization of clean matrices in M3(Z). Naresuan University Journal: Science and Technology (NUJST), [S.l.], v. 26, n. 1, p. 72-77, mar. 2018. ISSN 2539-553X. Available at: <https://www.journal.nu.ac.th/NUJST/article/view/1585>. Date accessed: 26 feb. 2024.