A note on the vanishing of certain local cohomology modules

For a finite module $M$ over a local, equicharacteristic ring $(R,m)$, we show that the well-known formula \cohdim(m,M)=\dim M becomes trivial if ones uses Matlis duals of local cohomology modules together with spectral sequences. We also prove a new, ring-theoretic vanishing criterion for local cohomology modules.Comment: 4 pages, submitted to CMB in 2009, to appea