E-Clean Matrices and Unit-Regular Matrices

Subject Areas : History and biography

Sh. A. Safari Sabet ¹ , S. Razaghi ²

1 - Department of Mathematics, Islamic Azad University, Central Tehran Branch,Code 14168-94351, Iran
2 - Department of Mathematics, Islamic Azad University, Central Tehran Branch,Code 14168-94351, Iran

Received: 2012-01-01 Accepted : 2012-01-01 Published : 2012-06-01

Keywords: Matrix ring, unimodular column, unit-regular, clean, e-clean,

Abstract :

Let $a, b, k,\in K$ and $u, v \in U(K)$. We show for any idempotent $e\in K$, $(a 0|b 0)$ise-clean iff $(a 0|u(vb + ka) 0)$is e-clean and if $(a 0|b 0)$is 0-clean, $(ua 0|u(vb + ka) 0)$is too.

References:

[1] V.P. Camillo, D. Khurana, A characterization of unit-regular rings, Comm. Algebra 29(2001) 2293-2295.

[2] V.P. Camillo, H.P.Yu, Exchange rings, units and idempotents, Comm. Algebra 22(1994) 4737-4749.

[3] D. Khurana,T.Y. Lam, Clean matrices and unit-regular matrices, J. Algebra 280(2004) 683-698.