A note on two-generated ideals over domains

摘要

Let R be a one-dimensional Noetherian domain and I be a two-generated fractional ideal of R. In this paper, we prove that I is SG-projective if and only if I and I−1 are equivalent, i.e. there exists a projective fractional ideal P of R such that I=I−1P. We also give an example to show that I being SG-projective does not necessarily imply that I and I−1 are isomorphic.