RESUMEN

In this paper we first compare the two generalizations of UFD’s due to Fletcher and Galovich. Utilizing the definition of a unique factorization ring and its structure theorem due to Fletcher we generalize some results on UFD’s. Furthermore, we show that the concepts of an irreducible element and a prime element in a UFR are equivalent. This helps us in generalizing some results of kaplansky. We also show that if R is a special PIR then R[x] is not a UFR. Two generalizations of unique factorization domains have been considered by Fletcher ([2], [3]) and Galovich [4]. Let R be a commutative ring with unity.