Castelnuovo's regularity of graded rings and modules (Q762225)

A numerical invariant of a graded module, suggested by a definition of Mumford for coherent sheaves on projective spaces, is introduced. In certain cases, notably that of a graded module over a Cohen-Macaulay algebra, A, over a field, the invariant bears a simple relationship to the invariant a(A) of Goto and Watanabe. The invariant is used to study minimal free resolutions of commutative Noetherian graded rings.