IDEALIZATIONS OF PSEUDO BUCHSBAUM MODULES OVER A PSEUDO BUCHSBAUM RING

Socles 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 ...

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.

Buchsbaum* 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...

An Auslander-buchsbaum Identity for Semi- Dualizing Modules

Descent from the Form Ring and Buchsbaum Rings

One of the major problems in commutative algebra is to recover information about a commutative ring A from known properties of the form ring G := GA(q) = ⊕n≥0q /q with respect to some ideal q of A. There are Krull’s classical results saying that A is an integral domain resp. a normal domain if G is an integral domain resp. a normal domain. It follows from the work [1], [2], [8] that several oth...