The Resolution of the Universal Ring for Finite Length Modules of Projective Dimension Two
نویسندگان
چکیده
Hochster established the existence of a commutative noetherian ring R and a universal resolution U of the form 0 ! R ! R ! R ! 0 such that for any commutative noetherian ring S and any resolution V equal to 0! S ! S ! S g ! 0, there exists a unique ring homomorphism R ! S with V = U R S. In the present paper we assume that f = e + g and we nd a resolution of R by free P-modules, where P is a polynomial ring over the ring of integers. For small values of e and g our resolution is a minimal resolution of R. For e and g both at least 5, we prove that R does not possess a generic minimal resolution.
منابع مشابه
Copresented Dimension of Modules
In this paper, a new homological dimension of modules, copresented dimension, is defined. We study some basic properties of this homological dimension. Some ring extensions are considered, too. For instance, we prove that if $Sgeq R$ is a finite normalizing extension and $S_R$ is a projective module, then for each right $S$-module $M_S$, the copresented dimension of $M_S$ does not exceed the c...
متن کاملUPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES
Let $R$ be a commutative Noetherian ring with non-zero identity and $fa$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properti...
متن کاملComplexes of $C$-projective modules
Inspired by a recent work of Buchweitz and Flenner, we show that, for a semidualizing bimodule $C$, $C$--perfect complexes have the ability to detect when a ring is strongly regular.It is shown that there exists a class of modules which admit minimal resolutions of $C$--projective modules.
متن کاملThe Auslander-Reiten Conjecture for Group Rings
This paper studies the vanishing of $Ext$ modules over group rings. Let $R$ be a commutative noetherian ring and $ga$ a group. We provide a criterion under which the vanishing of self extensions of a finitely generated $Rga$-module $M$ forces it to be projective. Using this result, it is shown that $Rga$ satisfies the Auslander-Reiten conjecture, whenever $R$ has finite global dimension and $ga...
متن کاملGorenstein 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