sentences:  Atomic domain
  
  In mathematics, more specifically ring theory, an atomic domain or factorization domain is an integral domain in which every non-zero non-unit can be written in at least one way as a finite product of irreducible elements.Atomic domains are different from unique factorization domains in that this decomposition of an element into irreducibles need not be unique; stated differently, an irreducible element is not necessarily a prime element.