3 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 $a\in\mathbb{F}_q^*$, and suppose the order of $x^n-a$ is $e=nz$. Constacyclic quotient-isomorphism conjecture. Then there is a ring isomorphism … This proposes an isomorphism…

Let $p=2$, let $k$ and $t$ be parameters with $0\le t\le 2^{k-1}-1$, and let $\alpha\in\mathbb F_{2^m}$ be nonzero. Consider polynomials $g(x)\in\mathbb F_{2^m}[x]$ satisfying … wi…