منابع مشابه
Auslander - Buchsbaum
A vanishing theorem is proved for Ext groups over non-commutative graded algebras. Along the way, an “infinite” version is proved of the non-commutative Auslander-Buchsbaum theorem.
متن کاملBuchsbaum* Complexes
A class of finite simplicial complexes, which we call Buchsbaum* over a field, is introduced. Buchsbaum* complexes generalize triangulations of orientable homology manifolds as well as doubly Cohen-Macaulay complexes. By definition, the Buchsbaum* property depends only on the geometric realization and the field. Characterizations in terms of simplicial homology are given. It is proved that Buch...
متن کاملOn Auslander-Buchsbaum - type formulas
We give a short and simple argument that proves, in a uniform way, the Auslander-Buchsbaum formula, relating depth and projective dimension, and the Auslander-Bridger formula, relating depth and G-dimension. Moreover, the same type of argument quickly reproves the fact that, in the degrees above the codepth, the syzygy modules of a finite module over a commutative local ring have no free summan...
متن کاملSocles of Buchsbaum modules, complexes and posets
The socle of a graded Buchsbaum module is studied and is related to its local cohomology modules. This algebraic result is then applied to face enumeration of Buchsbaum simplicial complexes and posets. In particular, new necessary conditions on face numbers and Betti numbers of such complexes and posets are established. These conditions are used to settle in the affirmative Kühnel’s conjecture ...
متن کاملA Generalization of the Auslander-buchsbaum Formula
Let R be a Noetherian local ring and Ω an arbitrary R-module of finite depth and finite projective dimension. The flat dimension of Ω is at least depth(R)−depth(Ω) with equality in the following cases: (i) Ω is finitely generated over some Noetherian local R-algebra S; (ii) dim(R) = 1; (iii) dim(R) = 2 and Ω is separated; (iv) R is CohenMacaulay, dim(R) = 3 and Ω is complete.
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ژورنال
عنوان ژورنال: Physics Today
سال: 1993
ISSN: 0031-9228,1945-0699
DOI: 10.1063/1.2809109