2 papers
math.AC2007
On vanishing of certain Ext modules
Shiro Goto, Futoshi Hayasaka, Ryo Takahashi
Let R be a Noetherian local ring with the maximal ideal m and dim R=1. In this paper, we shall prove that the module Ext^1_R(R/Q,R) does not vanish for every parameter ideal Q in R…
math.AC2006
Modules of reduction number one
Futoshi Hayasaka
Let (A, m) be a Noetherian local ring and N a parameter module in F=A^r and M=N:_F m the socle module of N. In this paper, we shall prove that the module M=N:_F m has a reduction n…