RINGS THAT ARE HOMOLOGICALLY OF MINIMAL MULTIPLICITY

Let R be a local Cohen-Macaulay ring with canonical module omega(R). We investigate the following question of Huneke: If the sequence of Betti numbers {beta(R)(i)(omega(R))} has polynomial growth, must R be Gorenstein? This question is well understood when R has minimal multiplicity. We investigate this question for a more general class of rings which we say are homologically of minimal multiplicity. We provide several characterizations of the rings in this class and establish a general ascent and descent result.