منابع مشابه
Of Module Structures , Vanishing of Ext , and Extended Modules
Let (R, m) and (S, n) be commutative Noetherian local rings, and let φ : R→ S be a flat local homomorphism such that mS = n and the induced map on residue fields R/m→ S/n is an isomorphism. Given a finitely generated R-module M , we show that M has an S-module structure compatible with the given R-module structure if and only if Ext R (S,M) = 0 for each i ≥ 1. We say that an S-module N is exten...
متن کاملOn a non-vanishing Ext
The existence of valuation domains admitting non-standard uniserial modules for which certain Exts do not vanish was proved in [1] under Jensen’s Diamond Principle. In this note, the same is verified using the ZFC axioms alone. In the construction of large indecomposable divisible modules over certain valuation domainsR, the first author used the property thatR satisfied Ext1R(Q,U) 6= 0, where ...
متن کاملVanishing of Ext-Functors and Faltings’ Annihilator Theorem for relative Cohen-Macaulay modules
et be a commutative Noetherian ring, and two ideals of and a finite -module. In this paper, we have studied the vanishing and relative Cohen-Macaulyness of the functor for relative Cohen-Macauly filtered modules with respect to the ideal (RCMF). We have shown that the for relative Cohen-Macaulay modules holds for any relative Cohen-Macauly module with respect to with ........
متن کاملSymmetry Theorems for Ext Vanishing
It was proved by Avramov and Buchweitz that if A is a commutative local complete intersection ring with finitely generated modules M and N , then the Ext groups between M and N vanish from some step if and only if the Ext groups between N and M vanish from some step. This paper shows that the same is true under the weaker conditions that A is Gorenstein and that M and N have finite complete int...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 2008
ISSN: 0025-5645
DOI: 10.2969/jmsj/06041045