On the distribution of prime divisors in class groups of affine monoid algebras
Victor Fadinger, Daniel Windisch
TL;DR
This paper studies the distribution of prime divisors in class groups of affine monoid algebras, extending previous results to show the abundance of prime divisors across classes in these algebraic structures.
Contribution
It generalizes Kainrath's result to a broader class of affine monoid algebras over fields, demonstrating the widespread presence of prime divisors in all classes.
Findings
Every finitely generated integral algebra of Krull dimension at least 2 over an infinite field has infinitely many prime divisors in all classes.
Extension of Kainrath's result to affine monoid algebras.
Prime divisors are distributed across all classes in the class groups of these algebras.
Abstract
We investigate the class groups and the distribution of prime divisors in affine monoid algebras over fields and thereby extend the result of Kainrath that every finitely generated integral algebra of Krull dimension at least 2 over an infinite field has infinitely many prime divisors in all classes.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsRings, Modules, and Algebras · Commutative Algebra and Its Applications · Homotopy and Cohomology in Algebraic Topology