 Moreover, a valuation domain with noncyclic (equivalently non-discrete) value group is not Noetherian, and every totally ordered abelian group is the value group of some valuation domain.This gives many examples of non-Noetherian Bézout domains.In noncommutative algebra, right Bézout domains are domains whose finitely generated right ideals are principal right ideals, that is, of the form "xR" for some "x" in "R".