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| Paper IPM / M / 726 | ||||||||||||||||||||||||||
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Let \fraka be an ideal of a commutative Noetherian ring R.
For finitely generated R-modules M and N with Supp
N ⊆ Supp M, it is shown that cd (\fraka,N) ≤ cd
(\fraka,M). Let N be a finitely generated module over a
local ring (R,\frak m) such that Min∧R∧N = Assh∧R∧N. Using the above result and the
notion of connectedness dimension, it is proved that cd
(\fraka,N) ≥ dimN−c(N/\fraka N)−1. Here c(N) denotes
the connectedness dimension of the topological space Supp N.
Finally, as a consequence of this inequality, two previously known
generalizations of Faltings' connectedness theorem are improved.
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