2007/01/19 by Mutsumi Saito, Ken Takahashi, Saito, Mutsumi +1
Computer Science · Mathematics · #13N10 #16S32 #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings and Algebras (math.RA) #math.RA #msc:13N10 #msc:16S32
paper · pdf · doi:10.48550/arxiv.math/0701529
21 pages
arxiv created 2007/01/19 · openalex publication_date 2007/01/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the Noetherian properties of the ring of differential operators of an affine semigroup algebra. First we show that it is always right Noetherian. Next we give a condition, based on the data of the difference between the semigroup and its scored closure, for the ring of differential operators being anti-isomorphic to another ring of differential operators. Using this, we prove that the ring of differential operators is left Noetherian if the condition is satisfied. Moreover we give some other conditions for the ring of differential operators being left Noetherian. Finally we conjecture necessary and sufficient conditions for the ring of differential operators being left Noetherian.