3 problems

Positive-answer conjecture. The question introduced in the source is conjectured to have a positive answer.

Double-extension conjecture. The algebra $B$ is a double extension.

Let $A$ be a ring, let $B$ be a double Ore extension of $A$ with generators $y_1,y_2$, and let $\sigma$ be its associated algebra map. Assume that $\sigma$ is invertible. Right-fre…