Integral domains in which each non‐zero ideal is divisorial

Let D be an integral domain with identity having quotient field K . A non-zero fractional ideal F of D is said to be divisorial if F is an intersection of principal fractional ideals of D [4; 2]. Equivalently, F is divisorial if there is a non-zero fractional ideal E of D such that Divisorial ideals arose in the investigations of Van der Waerden, Artin, and Krull in the 1930's and were called v -ideals by Krull [9; 118]. The concept has played an important role in the development of multiplicative ideal theory.