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An overring-theoretic approach to polynomial extensions of star and semistar operations

2010/04/25 by Gyu Whan Chang, Chang, Gyu Whan, Marco Fontana +1
Mathematics · Medicine · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #Spinal Hematomas and Complications #math.AC #math.AG

paper · pdf · doi:10.48550/arxiv.1004.4369

arxiv created 2010/04/25 · openalex publication_date 2010/04/25 · arxiv updated 2010/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Call a semistar operation ∗ on the polynomial domain D[X] an extension (respectively, a strict extension) of a semistar operation ⋆ defined on an integral domain D, with quotient field K, if E^⋆ = (E[X])∩ K (respectively, E^⋆ [X]= (E[X])) for all nonzero D-submodules E of K. In this paper, we study the general properties of the above defined extensions and link our work with earlier efforts, centered on the stable semistar operation case, at defining semistar operations on D[X] that are "canonical" extensions (or, "canonical" strict extensions) of semistar operations on D.

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