On the nil-clean matrix over a UFD

Document Type : Research Paper

Authors

Vali-e-Asr University of Rafsanjan

Abstract

 In this paper we characterize all $2\times 2$ idempotent and nilpotent matrices over an integral domain and then we characterize all $2\times 2$ strongly nil-clean matrices over a PID. Also, we determine when a $2\times 2$ matrix  over a UFD is nil-clean.

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References

[1] S. Breaz, G. Calugaranu, P. Danchev, T. Micu, Nil-clean matrix rings, Linear Algebra Appl., vol. 439, no. 1 (2013), 3115-3119.
[2] A. J. Diesl, Classes of strongly clean rings, Phd thesis, University of California, Berkeley, 2006.
[3] A. J. Diesl, Nil clean rings, J. Algebra, vol. 383, (2013), 197-211.
[4] T. W. Hungerford, Algebra, Springer-Verlag, 1980.
[5] M.T. Kossan, T. -K. Lee, Y. Zhou, When is every matrix over a division ring a sum of an idempotent and a nilpotent, Linear Algebra Appl., vol. 450 (2014), 7-12.
[6] W. K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc., vol. 229 (1977), 269-278.
[7] G. Song, X. Guo, Diagonability of idempotent matrices over noncommutative rings, Linear Algebra Appl., vol. 297, no. 1 (1999), 1-7.
Algebraic Structures and Their Applications
Volume 2, Issue 2
November 2015
Pages 49-55

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