Ore meets homothetic extensions

Abstract

Sufficient and necessary conditions for an extension of a skew-derivation $(\hat{I}{´}_R,\hat{I}{\pm }_R)$ of an associative $\mathbb{F}$-algebra $R$ to a skew derivation $(\hat{I}{´}_S,\hat{I}{\pm }_S)$ on an extension $S$ of $R$ by $\mathbb{F}$ or a {\em homothetic extension $S$ of $R$ by $\mathbb{F}$} are derived. It is then shown that this yields the unique extension of the Ore extension $R[x;\hat{I}{\pm }_R,\hat{I}{´}_R]$ of $R$ by $\mathbb{F}$ that embeds in the Ore extension $S[x;\hat{I}{\pm }_S,\hat{I}{´}_S]$ of $S$ by the extended skew-derivation.

12 pages