# Vanishing of Nil-terms and negative K-theory for additive categories

@article{Bartels2020VanishingON, title={Vanishing of Nil-terms and negative K-theory for additive categories}, author={Arthur Bartels and Wolfgang Lueck}, journal={arXiv: K-Theory and Homology}, year={2020} }

We extend notions such as Noetherian, regular, or regular coherent for rings to additive categories. We show that well-known properties for rings carry over to additive categories. For instance, the negative K-groups and all twisted Nil-groups vanish for an additive category if it is regular. Moreover, the additive category of twisted finite Laurent series associated to any automorphism of a Noetherian or regular additive category is again Noetherian or regular.

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