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arXiv · 2407.13119

The domain and prime properties for Koszul rings and algebras

Manuel L. Reyes·Daniel Rogalski
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Abstract

We establish a technique to prove that a Koszul graded ring is prime or a domain using information about its Koszul dual. This is based on a general categorical result that expands on methods of J.Y. Guo, which proves that certain orbital rings are prime or domains. We apply this method to prove that if $A = kQ/I$ is a Koszul twisted Calabi-Yau algebra of dimension 2, such that $Q$ is connected with every vertex having outdegree at least 2, then $A$ is a prime piecewise domain. In particular, the preprojective algebra of a connected quiver whose underlying graph has minimum degree at least 2 is a prime piecewise domain.

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Manuel L. Reyes, Daniel Rogalski. 2024-07-18. The domain and prime properties for Koszul rings and algebras. https://arxiv.org/abs/2407.13119

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