E-Clean Matrices and Unit-Regular Matrices
Subject Areas : History and biography
Sh. A. Safari Sabet
1
(Department of Mathematics, Islamic Azad University, Central Tehran Branch,Code
14168-94351, Iran)
S. Razaghi
2
(Department of Mathematics, Islamic Azad University, Central Tehran Branch,Code
14168-94351, Iran)
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.