Local--Global Properties for Semistar Operations

2003/05/14 by Marco Fontana, Fontana, Marco, Pascual Jara +3
Mathematics · #13F05 #13G05 #Advanced Topics in Algebra #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.math/0305202

openalex publication_date 2003/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the "local" behavior of several relevant properties concerning semistar operations, like finite type, stable, spectral, e.a.b. and a.b. We deal with the "global" problem of building a new semistar operation on a given integral domain, by "gluing" a given homogeneous family of semistar operations defined on a set of localizations. We apply these results for studying the local--global behavior of the semistar Nagata ring and the semistar Kronecker function ring. We prove that an integral domain D is a Prüfer ⋆--multiplication domain if and only if all its localizations D_P are Prüfer ⋆_P--multiplication domains.

Related

• The sets of star and semistar operations on semilocal Prüfer domains
• Nagata Rings, Kronecker Function Rings and Related Semistar Operations
• Universally catenarian integral domains, strong S-domains and semistar operations
• Uppers to zero and semistar operations in polynomial rings
• Polynomial extensions of semistar operations