On noncommutative bounded factorization domains and prime rings

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 prime to have Moreover, we construct (noncommutative) finitely presented semigroup algebra that an atomic does not satisfy ascending chain condition principal right or left ideals (ACCP), whence