sentences:  In an atomic domain, it is possible that different factorizations of the same element "x" have different lengths.It is even possible that among the factorizations of "x" there is no bound on the number of irreducible factors.If on the contrary the number of factors is bounded for every nonzero nonunit "x", then "R" is a bounded factorization domain (BFD); formally this means that for each such "x" there exists an integer "N" such that with none of the "x""i" invertible implies formula_1.