Some Results on Noetherian Warfield Domains

Let R be a domain. In this paper, we show that if R is one-dimensional, then R is a Noetherian Warfield domain if and only if every maximal ideal of R is 2-generated and for every maximal idealM of R, M is divisorial in the ring (M:M). We also prove that a Noetherian domain R is a Noetherian Warfield domain if and only if for every maximal ideal M of R, M2 can be generated by two elements. Finally, we give a sufficient condition under which all ideals of R are strongly Gorenstein projective.