相关论文: The Rees Valuations of Complete Ideals in a Regula…

Let I be a finitely supported complete m-primary ideal of a regular local ring (R, m). A theorem of Lipman implies that I has a unique factorization as a *-product of special *-simple complete ideals with possibly negative exponents for…

Let I be a finitely supported complete m-primary ideal of a regular local ring (R, m). We consider singularities of the normalization of the blow-up Proj R[It] of I. A theorem of Lipman implies that the ideal I has a unique factorization as…

In this paper, we introduce the notion of the strong Rees property (SRP) for $\mathfrak{m}$-primary ideals of a Noetherian local ring and prove that any power of the maximal ideal $\mathfrak{m}$ has its property if the associated graded…

In this paper, we study the $F$-rationality of the Rees algebra and the extended Rees algebra of $\mathfrak{m}$-primary ideals in excellent local rings $(R, \mathfrak{m})$ of prime characteristic. We partially answer some conjectures and…

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

Let $(R,\mathfrak{m})$ be a two-dimensional regular local ring with infinite residue class field. Then the Rees algebra $\mathcal{R} (I)= \bigoplus_{n \ge 0}I^n$ of $I$ is an almost Gorenstein graded ring in the sense of…

Let A and B be integral domains. Suppose A is Noetherian and B is a finitely generated A-algebra that contains A. Denote by A' the integral closure of A in B. We show that A' is determined by finitely many unique discrete valuation rings.…

By definition, an $\m$-primary ideal $I$ in a 2-dimensional regular local ring $(R, \m)$ is contracted if $I=R \cap IR[\m/x]$ for some $x \in \m \setminus \m^2$. Contracted ideals have been introduced by Zariski and used for proving the…

Let $I$ be a regular proper ideal in a Noetherian ring $R$, let $e \ge 2$ be an integer, let $\mathbf T_e = R[u,tI,u^{\frac{1}{e}}]' \cap R[u^{\frac{1}{e}},t^{\frac{1}{e}}]$ (where $t$ is an indeterminate and $u =\frac{1}{t}$), and let…

Let $(R,\mathfrak{M})$ be a two-dimensional regular local ring with algebraically closed residue field. Let $I$ be a simple complete $\mathfrak{M}$-primary ideal of $R$ and let $w$ denote its unique Rees valuation. Then the degree function…

A homogeneous ideal $I$ of a polynomial ring $S$ is said to have the Rees property if, for any homogeneous ideal $J \subset S $ which contains $I$, the number of generators of $J$ is smaller than or equal to that of $I$. A homogeneous ideal…

Let $R$ be a regular local ring of dimension at least 2. Associated to each valuation domain birationally dominating $R$, there exists a unique sequence $\{R_n\}$ of local quadratic transforms of $R$ along this valuation domain. We consider…

Many classical ring-theoretic results state that an ideal that is maximal with respect to satisfying a special property must be prime. We present a "Prime Ideal Principle" that gives a uniform method of proving such facts, generalizing the…

The authors introduced the notion of $p_g$-ideals for two-dimensional excellent normal local domain over an algebraicaly closed field in terms of resolution of singularities. In this note, we give several ring-theoretic characterization of…

We characterize ideals whose adjoints are determined by their Rees valuations. We generalize the notion of a regular system of parameters, and prove that for ideals generated by monomials in such elements, the integral closure and adjoints…

There has arisen in recent years a substantial theory of "multiplier ideals'' in commutative rings. These are integrally closed ideals with properties that lend themselves to highly interesting applications. But how special are they among…

We investigate when the Rees algebra of an integrally closed $\mathfrak{m}$-primary ideal in a regular local ring is a Cohen-Macaulay normal domain. While this property always holds in dimension two, it fails in general in higher…

Let $E$ be a module of projective dimension one over $R=k[x_1,\ldots,x_d]$. If $E$ is presented by a matrix $\varphi$ with linear entries and the number of generators of $E$ is bounded locally up to codimension $d-1$, the Rees ring…

In \cite{rees} Rees gave a characterization for the normal joint reduction number zero of two $\m$-primary ideals in an analytically unramified Cohen-Macaulay local ring of dimension two. Rees' result is a generalization of Zariski's…

This paper is about the local geometry of a real surfaces. It introduces machinery for studying families of subsets which are determined by conditions which are similar to base conditions, but also involve positivity/non-negativity. The…