Invariants of Cohen-Macaulay rings associated to their canonical ideals

The purpose of this paper is to introduce new invariants of Cohen-Macaulay local rings. Our focus is the class of Cohen-Macaulay local rings that admit a canonical ideal. Attached to each such ring R with a canonical ideal C, there are integers-the type of R, the reduction number of C-that provide valuable metrics to express the deviation of R from being a Gorenstein ring. We enlarge this list with other integers-the roots of R and several canonical degrees. The latter are multiplicity based functions of the Rees algebra of C.