Monomial methods in iterated local skew power series rings

2023/09/21 by Woods, Billy
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2309.11806

Abstract

Let A = \mathbbF_p or ℤ_p, and let R = A[[x₁]][[x₂; σ₂, δ₂]]…[[x_n;σ_n,δ_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 rank-2 local skew power series rings over \mathbbF_p satisfy polynormality, and give an example of a rank-2 local skew power series ring over ℤ_p which is a unique factorisation domain in the sense of Chatters-Jordan.

Related

• Dimension theory in iterated local skew power series rings
• Skew Generalized Power Series Rings With the McCoy Property
• Left-App rings of skew generalized power series
• S-Noetherian generalized power series rings
• Noetherian Skew Inverse Power Series Rings