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Paper IPM / M / 2945  


Abstract:  
We define two new homological invariants for a finitely generated
module M over a commutative Noetherian local ring R, its
Buchsbaum dimension Bdim_{R}M, and its Monomial conjecture
dimension MCdim_{R}M. It will be shown that these new invariants
have certain nice properties we have come to expect from
homological dimensions. Over a Buchsbaum ring R, every finite
module M has Bdim_{R}M < ∞; conversely, if the residue
field has finite Bdimension, then the ring R is Buchsbaum.
Similarly R satisfies the Hochster Monomial Conjecture if and
only if MCdim_{R}k is finite, where k is the residue field of
R. MCdimension fits between the Bdimension and restricted flat
dimension Rfd of [4]. Bdimension itself is finer than
CMdimension of [7] and we have equality if CMdimension is
finite. It also satisfies an analog of the AuslanderBuchsbaum
formula.
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