Home > Turkish Journal of Mathematics > Vol. 39 (2015) > No. 5
Turkish Journal of Mathematics
Uniquely strongly clean triangular matrices
HUANYIN CHEN
ORHAN GÜRGÜN
HANDAN KOSE
A ring $R$ is uniquely (strongly) clean provided that for any $a\in R$ there exists a unique idempotent $e\in R$ \big($e\in comm(a)$\big) such that $a-e\in U(R)$. We prove, in this note, that a ring $R$ is uniquely clean and uniquely bleached if and only if $R$ is abelian, ${\mathbb{T}}_{n}(R)$ is uniquely strongly clean for all $n\geq 1$, i.e. every $n\times n$ triangular matrix over $R$ is uniquely strongly clean, if and only if $R$ is abelian, and ${\mathbb{T}}_{n}(R)$ is uniquely strongly clean for some $n\geq 1$. In the commutative case, more explicit results are obtained.
Uniquely strongly clean ring, uniquely bleached ring, triangular matrix ring
CHEN, HUANYIN; GÜRGÜN, ORHAN; and KOSE, HANDAN (2015) "Uniquely strongly clean triangular matrices," Turkish Journal of Mathematics: Vol. 39: No. 5, Article 4. https://doi.org/10.3906/mat-1408-13
Available at: https://journals.tubitak.gov.tr/math/vol39/iss5/4
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