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Paper   IPM / M / 2945
School of Mathematics
  Title:   Buchsbaum and monomial conjecture dimension
1.  J. Asadollahi
2.  Sh. Salarian
  Status:   Published
  Journal: Comm. Algebra
  Vol.:  32
  Year:  2004
  Pages:   3969-3979
  Supported by:  IPM
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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