Abstract
Let R be a Noetherian ring, M an Artinian R-module, and 𝖒 ∈ Cos RM. Then cograde R𝔭 Hom R (R𝔭,M) = inf {i | πi(𝔭,M) > 0} and [Formula: see text] where πi(𝔭,M) is the i-th dual Bass number of M with respect to 𝔭, cograde R𝔭 Hom R (R𝔭,M) is the common length of any maximal Hom R (R𝔭, M)-quasi co-regular sequence contained in 𝔭 R𝔭, and fd R𝔭 Hom R (R𝔭, M) is the flat dimension of the R𝔭-module Hom R (R𝔭, M). We also study the relations among cograde, co-dimension and flat dimension of co-localization modules.
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