Integrally closed rings in birational extensions of two-dimensional regular local rings

Let $D$ be an integrally closed local Noetherian domain of Krull dimension 2, and let $f$ be a nonzero element of $D$ such that $fD$ has prime radical. We consider when an integrally closed ring $H$ between $D$ and $D_f$ is determined locally by finitely many valuation overrings of $D$. We show such a local determination is equivalent to a statement about the exceptional prime divisors of normalized blow-ups of $D$, and, when $D$ is analytically normal, this property holds for $D$ if and only if it holds for the completion of $D$. This latter fact, along with MacLane's notion of key polynomials, allows us to prove that in some central cases where $D$ is a regular local ring and $f$ is a regular parameter of $D$, then $H$ is determined locally by a single valuation. As a consequence, we show that if $H$ is also the integral closure of a finitely generated $D$-algebra, then the exceptional prime ideals of the extension $H/D$ are comaximal. Geometrically, this translates into a statement about intersections of irreducible components in the closed fiber of the normalization of a proper birational morphism.Comment: 32 pp., to appear in Math. Proc. Camb. Phil. So

Star-Invertibility and tt-finite character in Integral Domains

Let $A$ be an integral domain. We study new conditions on families of integral ideals of $A$ in order to get that $A$ is of $t$-finite character (i.e., each nonzero element of $A$ is contained in finitely many $t$-maximal ideals). We also investigate problems connected with the local invertibility of ideals.Comment: 16 page

Essential properties for rings of integer-valued polynomials

Let D be an integral domain with quotient field K. We consider the ring of integer-valued polynomials over D, namely, Int(D) ∶= {f ∈ K[X]; f(D) ⊆ D}. In this paper we investigate when Int(D) has essentialtype properties. In particular, we give a complete characterization of when Int(D)is locally essential, locally PvMD, locally UFD, locally GCD, Krull-type or generalized Krull

Invertibility of ideals in prüfer extensions

Using the general approach to invertibility for ideals in ring extensions given by Knebush and Zhang in [9], we investigate about connections between faithfully atness and invertibility for ideals in rings with zero divisors

INTEGRALLY CLOSED RINGS IN BIRATIONAL EXTENSIONS OF TWO-DIMENSIONAL REGULAR LOCAL RINGS

Abstract. Let D be an integrally closed local Noetherian domain of Krull dimension 2, and let f be a nonzero element of D such that f D has prime radical. We consider when an integrally closed ring H between D and D f is determined locally by finitely many valuation overrings of D. We show such a local determination is equivalent to a statement about the exceptional prime divisors of normalized blow-ups of D, and, when D is analytically normal, this property holds for D if and only if it holds for the completion of D. This latter fact, along with MacLane's notion of key polynomials, allows us to prove that in some central cases where D is a regular local ring and f is a regular parameter of D, then H is determined locally by a single valuation. As a consequence, we show that if H is also the integral closure of a finitely generated D-algebra, then the exceptional prime ideals of the extension H/D are comaximal. Geometrically, this translates into a statement about intersections of irreducible components in the closed fiber of the normalization of a proper birational morphism

"I'm not my disease": the choice to talk about their cancer experience by common women or female celebrities

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Clinical and radiographic mid-term outcomes after total shoulder replacement: a retrospective study protocol including 400 anatomical and reverse prosthetic implants

Objectives: To obtain outcomes data on anatomical and reverse total shoulder arthroplasty by analysis of clinical scores and standard radiographs. Subject selection and enrollment: 400 consecutive series of patients replaced with anatomical and reverse total shoulder arthroplasty (minimum 3 years follow-up). Study Design: retrospective monocenter. Preoperative assessment: Demographics, clinical scores (Constant-Murley) as available, shoulder X-ray (AP, outlet and axillary views) . Last follow-up: Postoperative radiographhs and clinical scores. Adverse events and complications to be reported as occurred since implantation. Statistical analysis: Data collected will be summarized and analyzed for statistical significance

Should we continue to study high-dose chemotherapy in metastatic breast cancer patients? A critical review of the published data

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