Monomial methods in iterated local skew power series rings
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 Gröbner bases for $R$. We show that all rank2 local skew power series rings over $\mathbb{F}_p$ satisfy polynormality, and give an example of a rank2 local skew power series ring over $\mathbb{Z}_p$ which is a unique factorisation domain in the sense of ChattersJordan.
 Publication:

arXiv eprints
 Pub Date:
 September 2023
 DOI:
 10.48550/arXiv.2309.11806
 arXiv:
 arXiv:2309.11806
 Bibcode:
 2023arXiv230911806W
 Keywords:

 Mathematics  Rings and Algebras
 EPrint:
 31 pages with 3 figures. Draft: comments welcome