On q-skew Iterated Ore Extensions Satisfying a Polynomial Identity

TL;DR

This paper introduces an elementary method to analyze q-skew iterated Ore extensions satisfying polynomial identities, simplifying derivation removal and extending known results about PI properties in such algebraic structures.

Contribution

It provides a new elementary approach to erasing derivations in PI q-skew Ore extensions and establishes conditions under which the extension remains PI.

Findings

Elementary derivation erasure method for PI q-skew Ore extensions

Extension existence and PI property transfer under mild conditions

Recovery and extension of results by Haynal (2008)

Abstract

For iterated Ore extensions satisfying a polynomial identity we present an elementary way of erasing derivations. As a consequence we recover some results obtained by Haynal in "PI degree parity in q-skew polynomial rings" (J. Algebra 319, 2008, 4199-4221). We also prove, under mild assumptions on $R_n=R[x_1;\si_1,\de_1]...[x_n;\si_n;\de_n]$ that the Ore extension $R[x_1;\si_1]...[x_n;\si_n]$ exists and is PI if $R_n$ is PI.