THE HOMOLOGICAL DEGREE OF A MODULE

A homological degree of a graded module M is an extension of the usual notion of multiplicity tailored to provide a numerical signature for the module even when M is not Cohen-Macaulay. We construct a degree, h deg(M), that behaves well under hyperplane sections and the modding ou t of elements of finite support. When carried out in a local algebra t his degree gives a simulacrum of complexity a la Castelnuovo-Mumford's regularity. Several applications for estimating reduction numbers of ideals and predictions on the outcome of Noether normalizations are gi ven.