The space of homogeneous preserving semistar operations on graded domains
type: Item
instance of: scholarly article
title: The space of homogeneous preserving semistar operations on graded domains
zbMATH Open document ID: 1503.13001
author: Parviz Sahandi
published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
publication date: 2022-10-12T00:00:00Z
review text: In this paper, the author studies the space of homogeneous preserving semistar operations on a graded ring \(R=\displaystyle\bigoplus_{\alpha\in \Gamma}R_{\alpha}\) graded by an arbitrary grading torsionless monoid \(\Gamma\). The main result states that the set \(SStar_{f, hp}(R)\) of finite type, homogeneous preserving semistar operations on \(R\), endowed with the Zariski topology, is a spectral space.
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13G05
Mathematics Subject Classification ID: 13F05
zbMATH DE Number: 7600346
zbMATH Keywords: semistar operation
zbMATH Keywords: homogeneous preserving semistar operation
zbMATH Keywords: Kronecker function ring
zbMATH Keywords: graded domain
zbMATH Keywords: Gr-valuation domain
zbMATH Keywords: spectral space
reviewed by: A. Mimouni
MaRDI profile type: Publication
full work available at URL: s13398-022-01277-7
OpenAlex ID: W4285089462
cites work: Divisibility Properties of Graded Domains
cites work: Examples of star operations on integral domains
cites work: Graded-valuation domains
cites work: Graded integral domains and Nagata rings
cites work: Integer-valued polynomials and Prüfer \(v\)-multiplication domains
cites work: Kronecker function rings and abstract Riemann surfaces
cites work: Projective star operations on polynomial rings over a field
cites work: Spectral Spaces and Ultrafilters
cites work: The constructible topology on spaces of valuation domains
cites work: Spectral spaces of semistar operations
cites work: Some topological considerations on semistar operations
cites work: Localizing systems and semistar operations
cites work: PRÜFER ⋆-MULTIPLICATION DOMAINS AND SEMISTAR OPERATIONS
cites work: Cancellation properties in ideal systems: A classification of e.a.b. semistar operations
cites work: The Patch Topology and the Ultrafilter Topology on the Prime Spectrum of a Commutative Ring
cites work: Nagata Rings, Kronecker Function Rings, and Related Semistar Operations
cites work: A Krull-type theorem for the semistar integral closure of an integral domain
cites work: Kronecker function rings: A general approach.
cites work: Q3436764
cites work: On some classes of integral domains defined by Krull's \(a.b.\) operations
cites work: Q5661989
cites work: Kronecker Function Rings and Generalized Integral Closures
cites work: Prime Ideal Structure in Commutative Rings
cites work: Q3283972
cites work: The graded ring \(R[X_1,\dots,X_n\)
cites work: Integral closure and generalized transforms in graded domains
cites work: Beiträge zur Arithmetik kommutativer Integritätsbereiche. II. \(v\)- Ideale und vollständig ganz abgeschlossene Integritätsbereiche
cites work: Q5542855
cites work: Q4328016
cites work: Noetherian Spaces of Integrally Closed Rings with an Application to Intersections of Valuation Rings
cites work: CHARACTERIZATIONS OF GRADED PRÜFER ⋆-MULTIPLICATION DOMAINS
cites work: Characterizations of graded Prüfer \(\star \)-multiplication domains. II
cites work: Q4071851
DOI: 10.1007/S13398-022-01277-7
description: scientific article; zbMATH DE number 7600346