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arXiv · 2309.11806

Monomial methods in iterated local skew power series rings

Billy Woods
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Abstract

Let $A = \mathbb{F}_p$ or $\mathbb{Z}_p$, and let $R = A[[x_1]][[x_2; \sigma_2, \delta_2]]\dots[[x_n;\sigma_n,\delta_n]]$, an iterated local skew power series ring over $A$. Under mild conditions, we show that (multiplicative) monomial orders exist, and develop the theory of Gr\"obner bases for $R$. We show that all rank-2 local skew power series rings over $\mathbb{F}_p$ satisfy polynormality, and give an example of a rank-2 local skew power series ring over $\mathbb{Z}_p$ which is a unique factorisation domain in the sense of Chatters-Jordan.

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Billy Woods. 2023-09-21. Monomial methods in iterated local skew power series rings. https://arxiv.org/abs/2309.11806

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