Differential smoothness of skew polynomial rings

TL;DR

This paper proves that the property of differential smoothness is preserved under tensor products and skew polynomial extensions of certain algebras, expanding understanding of their structural stability.

Contribution

It establishes that tensor products and skew polynomial rings over differentially smooth algebras remain differentially smooth under natural conditions.

Findings

Tensor products of differentially smooth algebras are differentially smooth.

Skew polynomial rings over differentially smooth algebras are differentially smooth.

Results apply under natural assumptions on the algebras.

Abstract

It is shown that, under some natural assumptions, the tensor product of differentially smooth algebras and the skew-polynomial rings over differentially smooth algebras are differentially smooth.