Strongly clean triangular matrix rings over local rings
By Gautam Borooah, A. Diesl, Thomas J. Dorsey. 2007
47 citations recorded by the source corpus.
Abstract An element of a ring is called strongly clean if it can be written as the sum of a unit and an idempotent that commute. A ring is called strongly clean if each of its elements is strongly clean. In this paper, we investigate conditions on a local ring R that imply that T n ( R ) is a strongly clean ring. It is shown that this is the case for commutative local rings R, as well as for a host of other classes of local rings. An example of a local ring A for which T 2 ( A ) is not strongly clean is also given.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/84bb7d9e47cede638b5d1385486a01eed112d950
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In Algebra and Number Theory
In Geometry and Topology
Citations in the corpus
- Strongly clean matrix rings over commutative local rings (2008, background): “The related question of when Tn(R), the ring of upper triangular matrices over R, is strongly clean is addressed in [21] (for n = 2, R local), [25] (for R = Z(2)), in [9], and by the present authors in [3] (for arbitrary n, R local).”
- Pseudo Drazin inverses in associative rings and Banach algebras (2012, background): “Furthermore, if both lu − rj and lj − ru are isomorphic, then we say that R is uniquely bleached (see [4]).”
- On Strongly J-Clean Rings (2010, background): “(1) R is a uniquely clean ring; (2) R is a strongly J -clean with all idempotents central; (3) Every homomorphic image of R is a uniquely clean ring.”