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5 papers · 2 filters
The structure of Sally modules of rank one
Shiro Goto, Koji Nishida, Kazuho Ozeki
A complete structure theorem of Sally modules of $\fkm$-primary ideals in a Cohen-Macaulay local ring $(A, \m)$ satisfying the equality $\e_1(I)=\e_0(I)-\ell_A(A/I)+1$ is given…
Quasi-socle ideals in Gorenstein numerical semigroup rings
Shiro Goto, Satoru Kimura, Naoyuki Matsuoka
Quasi-socle ideals, that is the ideals of the form in Gorenstein numerical semigroup rings over fields are explored, where is a parameter ideal, and…
A local ring such that the map between Grothendieck groups with rational coefficient induced by completion is not injective
Kazuhiko Kurano, Vasudevan Srinivas
In this paper, we construct a local ring such that the kernel of the map $G_0(A)\subq \to G_0(\hat{A})\subq$ is not zero, where is the comletion of with respect t…
Direct summands of syzygy modules of the residue class field
Ryo Takahashi
Let R be a commutative Noetherian local ring. This paper deals with the problem asking whether R is Gorenstein if the n-th syzygy of the residue field of R has a nontrivial direct…
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…