Regular sequences and ZD-modules
Abstract
Let R be a Noetherian ring, I an ideal of R and M a ZD-module. Let S be a Melkersson subcategory with respect to I such that M/IM doesn't belong to S. We show that all maximal S-sequences on M in I, have equal length. If this common length is denoted by S-depthI(M), then S-depthI(M) = infi : HiI(M) doesn't belong to S.
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