strongly clean triangular matrix rings with endomorphisms

نویسندگان

h. chen

h. kose

y. ‎kurtulmaz

چکیده

‎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. ‎further‎, ‎$t_3(r,sigma)$ is strongly clean if‎ ‎$l_{a}-r_{sigma(b)}‎, ‎l_{a}-r_{sigma^2(b)}$ and‎ ‎$l_{b}-r_{sigma(a)}$ are surjective for any $ain u(r),bin‎ ‎j(r)$‎. ‎the necessary condition for $t_3(r,sigma)$ to be strongly‎ ‎clean is also obtained‎. ‎

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Strongly clean triangular matrix rings with endomorphisms

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عنوان ژورنال:
bulletin of the iranian mathematical society

ناشر: iranian mathematical society (ims)

ISSN 1017-060X

دوره 41

شماره 6 2015

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