Y. Kurtulmaz
Department of Mathematics, Bilkent University, Ankara, Turkey.
[ 1 ] - Very cleanness of generalized matrices
An element $a$ in a ring $R$ is very clean in case there exists an idempotent $ein R$ such that $ae = ea$ and either $a- e$ or $a + e$ is invertible. An element $a$ in a ring $R$ is very $J$-clean provided that there exists an idempotent $ein R$ such that $ae = ea$ and either $a-ein J(R)$ or $a + ein J(R)$. Let $R$ be a local ring, and let $sin C(R)$. We prove that $Ain K_...
[ 2 ] - Strongly clean triangular matrix rings with endomorphisms
A ring $R$ is strongly clean provided that every element in $R$ is the sum of an idempotent and a unit that commutate. Let $T_n(R,sigma)$ be the skew triangular matrix ring over a local ring $R$ where $sigma$ is an endomorphism of $R$. We show that $T_2(R,sigma)$ is strongly clean if and only if for any $ain 1+J(R), bin J(R)$, $l_a-r_{sigma(b)}: Rto R$ is surjective. Furt...