Gorenstein rings through face rings of manifolds

نویسندگان

  • Isabella Novik
  • Ed Swartz
چکیده

The face ring of a homology manifold (without boundary) modulo a generic system of parameters is studied. Its socle is computed and it is verified that a particular quotient of this ring is Gorenstein. This fact is used to prove that the sphere g-conjecture implies all enumerative consequences of its far reaching generalization (due to Kalai) to manifolds. A special case of Kalai’s manifold g-conjecture is established for homology manifolds that have a codimension-two face whose link contains many vertices.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

un 2 00 8 Gorenstein rings through face rings of manifolds

The face ring of a homology manifold (without boundary) modulo a generic system of parameters is studied. Its socle is computed and it is verified that a particular quotient of this ring is Gorenstein. This fact is used to prove that the sphere gconjecture implies all enumerative consequences of its far reaching generalization (due to Kalai) to manifolds. A special case of Kalai’s manifold g-co...

متن کامل

AN EXTENDED NOTION OF THE GRADE OF AN IDEAL, AND GORENSTEIN RINGS

In this paper we shall apply modules of generalized fractions to extend the notion of the grade of an ideal, and to obtain characterizations of Gorenstein rings.

متن کامل

GENERALIZED GORENSTEIN DIMENSION OVER GROUP RINGS

Let $(R, m)$ be a commutative noetherian local ring and let $Gamma$ be a finite group. It is proved that if $R$ admits a dualizing module, then the group ring $Rga$ has a dualizing bimodule as well. Moreover, it is shown that a finitely generated $Rga$-module $M$ has generalized Gorenstein dimension zero if and only if it has generalized Gorenstein dimension zero as an $R$-module.

متن کامل

Gorenstein homological dimensions with respect to a semi-dualizing module over group rings

Let R be a commutative noetherian ring and Γ a finite group. In this paper,we study Gorenstein homological dimensions of modules with respect to a semi-dualizing module over the group ring  . It is shown that Gorenstein homological dimensions  of an  -RΓ module M with respect to a semi-dualizing module,  are equal over R and RΓ  .

متن کامل

Gorenstein hereditary rings with respect to a semidualizing module

‎Let $C$ be a semidualizing module‎. ‎We first investigate the properties of‎ ‎finitely generated $G_C$-projective modules‎. ‎Then‎, ‎relative to $C$‎, ‎we introduce and study the rings over which‎ ‎every submodule of a projective (flat) module is $G_C$-projective (flat)‎, ‎which we call $C$-Gorenstein (semi)hereditary rings‎. ‎It is proved that every $C$-Gorenstein hereditary ring is both cohe...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008