5 problems

Let $S$ be a ring with automorphism $\sigma$, let $f(t)$ be the polynomial defining the source quotient, and let $a,b\truein S$ and $\mathbf{m},\mathbf{n}$ be the associated parame…

Let $R$ be a ring, let $\sigma$ be an endomorphism of $R$, and let $V_n(R)$ denote the relevant skew polynomial ring construction with induced endomorphism $\bar\sigma$. Strong sym…

Let $\Bbbk$ be a field with $\operatorname{char}\;\Bbbk\neq 2$, let $A=\Bbbk_{-1}[x_1,\ldots,x_n]^{(v)}$ be the $v$th Veronese subring of the skew polynomial ring, where $v$ is a p…

Binomial-ring generation conjecture. Every square-free solution of finite order can be "generated" from a binomial ring with skew polynomial relation.

Let $B$ be a quantum polynomial ring and let $G$ be a finite subgroup of $\operatorname{Aut_{gr}}(B)$. Noncommutative Shephard–Todd–Chevalley conjecture. The fixed subring $B^G$ ha…