Minimal Prime Ideals and Semistar Operations

2008/09/08 by Parviz Sahandi, Sahandi, Parviz
Computer Science · Mathematics · #13A15 #13G05 #Advanced Algebra and Logic #Advanced Topics in Algebra #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras #math.AC #msc:13A15 #msc:13G05

paper · pdf · doi:10.48550/arxiv.0809.1307

Accepted in the Rocky mountain Journal Math

openalex publication_date 2008/09/08 · arxiv created 2008/12/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a commutative integral domain and let ⋆ be a semistar operation of finite type on R, and I be a quasi-⋆-ideal of R. We show that, if every minimal prime ideal of I is the radical of a ⋆-finite ideal, then the set \Min(I) of minimal prime ideals over I is finite.

Related

• Radical semistar operations
• A look at the prime and semiprime operations of one-dimensional domains
• Generalized prime ideals of the rings C(X,Y) and the quasi-components of X
• Towards a classification of stable semistar operations on a Pr "ufer\n domain
• On rings for which finitely generated ideals have only finitely many components