On NI and NJ skew PBW extensions

TL;DR

This paper investigates conditions under which skew PBW extensions are NI or NJ rings, extending known results from skew polynomial rings to broader classes like universal enveloping algebras and differential operators.

Contribution

It provides necessary and sufficient conditions for skew PBW extensions to be NI or NJ rings, broadening the understanding of their algebraic properties.

Findings

Established conditions for skew PBW extensions to be NI or NJ rings

Extended results from skew polynomial rings to universal enveloping algebras

Applied findings to differential operator examples

Abstract

We establish necessary or sufficient conditions to guarantee that skew Poincar\'e-Birkhoff-Witt extensions are NI or NJ rings. Our results extend those corresponding for skew polynomial rings and establish similar properties for other families of noncommutative rings such as universal enveloping algebras and examples of differential operators.