Z-Graded Rings and Modules

This chapter contains some general facts about graded rings that arise in connection with blowing up. We compute the dimensions of these rings and for certain cases we construct special systems of parameters. We also relate the multiplicities and Hilbert functions of the original ring to those of the various graded rings derived from it. Then we recall the theory of standard bases, and finally we show how to translate some well known results on flatness to the graded case. Our presentation uses also ideas of the unpublished thesis of E.C. Dade [5].