On the Intersection Algebra of Principal Ideals

2013/02/01 by Sara Malec, Malec, Sara
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC

paper · pdf · doi:10.48550/arxiv.1302.0312

Minor changes, to appear in Communications in Algebra

openalex publication_date 2013/02/01 · arxiv created 2013/09/20 · arxiv updated 2013/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the finite generation of the intersection algebra of two principal ideals I and J in a unique factorization domain R. We provide an algorithm that produces a list of generators of this algebra over R. In the special case that R is a polynomial ring, this algorithm has been implemented in the commutative algebra software system Macaulay2. A new class of algebras, called fan algebras, is introduced.

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