FREE RESOLUTIONS AND CHANGE OF RINGS

Projective resolutions of modules over a ring R are constructed starti ng from appropriate projective resolutions over a ring Q mapping to R. It is shown that such resolutions may be chosen to be minimal in codi mension less than or equal to 2, but not in codimension 3. This is use d to obtain minimal resolutions for essentially all modules over local (or graded) rings R with codimension less than or equal to 2. Explici t resolutions are given for cyclic modules over multigraded rings, and necessary and sufficient conditions are obtained for their minimality . (C) 1997 Academic Press.