RINGS IN WHICH ELEMENTS ARE UNIQUELY THE SUM OF AN IDEMPOTENT AND A UNIT

By W. K. Nicholson, Yiqiang Zhou. Glasgow Mathematical Journal, 2004

159 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/835f46e2d7210a533f4377ffea60ddb435804a8e

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In Algebra and Number Theory

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Citations in the corpus

Commutative weakly nil clean unital rings (2015, background): “Later on, in [24] the authors study such arbitrary rings, again calling them uniquely clean; notice that this uniqueness is tantamount to the existence of a unique idempotent with the given sum property (see [6]).”
Graphs Attached to Rings Revisited (2011, background): “In [29], the authors proved that the ring R is uniquely clean if and only if |R/m| = 2 for each maximal ideal m of R.”
Clean general rings (2005, background): “Recall [11] that a ring R is said to be uniquely clean if every element of R can be written uniquely as the sum of an idempotent and a unit.”
Unit Graphs Associated with Rings (2010, background): “In [15] the authors proved that the ring R is uniquely clean if and only if for each maximal ideal of R, R/ = 2.”
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 [ 17 ] (for n = 2, R local), [21] (for R = Z(2)), and by the present authors in [3] (for arbitrary n, R local).”
Rings in which every element is either a sum or a difference of a nilpotent and an idempotent (2014, background): “However, by a combination of Theorem 12 with results from [17], one can infer the surprising fact that a uniquely weakly nil-clean ring is not necessarily uniquely clean, and hence not necessarily uniquely nil-clean.”
Strongly clean triangular matrix rings over local rings (2007, background): “A ring R is uniquely (strongly) clean if for all a ∈ R there is a unique e2 = e ∈ R such that a is (strongly) e-clean (see [17]).”
Pseudo Drazin inverses in associative rings and Banach algebras (2012, background): “The idea of the proof of Lemma 2.5 suggests us to complete the Nicholson–Zhou observation in [21].”
On Strongly J-Clean Rings (2010, unknown): “[10]).”