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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.
ACKNOWLEDGMENTS
The author thanks her advisor, Florian Enescu, for many fruitful discussions, as well as Yongwei Yao for his useful suggestions.
Notes
Communicated by G. Leuschke.