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| Paper IPM / M / 2945 |
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| Abstract: | |||||
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We define two new homological invariants for a finitely generated
module M over a commutative Noetherian local ring R, its
Buchsbaum dimension B-dimRM, and its Monomial conjecture
dimension MC-dimRM. 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 B-dimRM < ∞; conversely, if the residue
field has finite B-dimension, then the ring R is Buchsbaum.
Similarly R satisfies the Hochster Monomial Conjecture if and
only if MC-dimRk is finite, where k is the residue field of
R. MC-dimension fits between the B-dimension and restricted flat
dimension Rfd of [4]. B-dimension itself is finer than
CM-dimension of [7] and we have equality if CM-dimension is
finite. It also satisfies an analog of the Auslander-Buchsbaum
formula.
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