A ring has bounded factorizations if every cancellative nonunit a∈R can be written as a product of atoms and there is bound λ(a) on the lengths such factorizations. The factorization property one most basic finiteness properties in study non-unique Every commutative noetherian domain factorizations, but it open whether result holds noncommutative setting. We provide sufficient conditions for pr...

An element in a ring is called clean if it may be written as a sum of a unit and idempotent. The ring itself is called clean if every element is clean. Recently, Anderson and Camillo (Anderson, D. D., Camillo, V. (2002). Commutative rings whose elements are a sum of a unit and an idempotent. Comm. Algebra 30(7):3327–3336) has shown that for commutative rings every von-Neumann regular ring as we...