The notion of almost Gorenstein local ring introduced by V. Barucci and R. Fröberg for one-
dimensional Noetherian local rings which are analytically unramified has been generalized …

Let (A, m) be a Cohen–Macaulay local ring, and let I be an ideal of A. We prove that the
Rees algebra R (I) is an almost Gorenstein ring in the following cases:(1)(A, m) is a two …

Let $ A $ be a two-dimensional excellent normal Gorenstein local domain. In this paper, we
characterize elliptic ideals $ I\subset A $ for its normal tangent cone $\overline {G}(I) $ to be …

Let I be an m-primary ideal of a Noetherian local ring (R, m). We consider the Gorenstein
and complete intersection properties of the associated graded ring G (I) and the fiber cone F …

This paper gives a necessary and sufficient condition for Gorensteinness in Rees algebras
of the d th power of parameter ideals in certain Noetherian local rings of dimension d≥ 2 …

The aim of this paper is to elucidate the relationship between the Gorenstein Rees algebra
$\R (I):=\bigoplus_ {i\ge 0} I^ i $ of an ideal $ I $ in a complete Noetherian local ring $ A …

Let $ R $ be a Noetherian local ring with the maximal ideal $\mathfrak {m} $. Assume that $
R $ contains ideals $ I $ and $ J $ satisfying the conditions (1) $ I\subseteq J $,(2) …

Let (R, m) be a Cohen–Macaulay local ring, and let ℱ={F i} i∈ ℤ be an F 1-good filtration of
ideals in R. If F 1 is m-primary we obtain sufficient conditions in order that the associated …

In this article, we study the Castelnuovo–Mumford regularity and Gorenstein properties of
the fiber cone. We obtain upper bounds for the Castelnuovo–Mumford regularity of the fiber …

Let $ A $ be a regular local ring and let $\mathcal {F}=\{F_ {n}\} _ {n\in\mathbb {Z}} $ be a
filtration of ideals in $ A $ such that $\mathcal {R}(\mathcal {F})=\bigoplus _ {n\geq 0} F_ {n} …