Generalized GCD rings.
Let be a ring extension of . We show the left -module with the endmorphism ring End is a generalized tilting module when is a generalized tilting module under some conditions.
We characterize the postulation character of arithmetically Gorenstein curves in P4. We give conditions under which the curve can be realized in the form mH - K on some ACM surface. Finally, we complement a theorem by Watanabe by showing that any general arithmetically Gorenstein curve in P4 with arbitrary fixed postulation character can be obtained from a line by a series of ascending complete-intersection biliaisons.