Gabriel dimension of graded rings
Let and be two ring homomorphisms and let and be ideals of and , respectively, such that . In this paper, we investigate the transfer of the notions of Gaussian and Prüfer rings to the bi-amalgamation of with along with respect to (denoted by introduced and studied by S. Kabbaj, K. Louartiti and M. Tamekkante in 2013. Our results recover well known results on amalgamations in C. A. Finocchiaro (2014) and generate new original examples of rings possessing these properties.
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.