Projective dimension in UFDs

A characterization of factorial Noetherian domains in terms of O-submodules is presented and it is applied to give a criterion for the ring of a hypersurface to be factorial (Vasconcelos, Computational Methods in Commutative Algebra and Algebraic Geometry, Springer, Berlin, 1998) and to reduce a conjecture of Evans and Griffith in Syzygies (Cambridge University Press, Cambridge, UK, 1985) to ideals. (C) 2000 Elsevier Science B.V. All rights reserved. MSC. Primary 13C15; secondary 13C14, 13H10