8 problems

Let the codes under consideration be special cases of Sheekey's constructed codes, and let the Galois group involved have different possible generators. Generator-dependence conjec…

Let a semifield be a finite algebra whose multiplication tensor has BEL rank equal to the minimum matrix rank among tensors that are $S_3$-equivalent to it. For a semifield of dime…

Let $v,w$ be elements of the Weyl group in the setting of the flag manifold over the semifield $\mathbb Z$, and let $[[v,w]]$ denote the set defined in type $A_2$ by the cited cons…

A finite presemifield is an algebraic structure whose multiplication is distributive over addition and has no zero divisors; semifields are isotopic to presemifields, and two prese…

A semifield is a finite-dimensional, not necessarily associative division algebra over a finite field; its order is its number of elements. Kantor's conjecture. The number of semif…

A semifield is a commutative semiring whose multiplicative structure is a group. A semiring is finitely generated as a semiring when it is generated by finitely many elements under…

Let $F$ be a field of finite transcendence degree over $\mathbb{Q}$ or over a finite field. Abhyankar's theorem represents $F$ as a homomorphic image of a subring of a polynomial r…

Inequivalent DHO count conjecture. The number of pairwise inequivalent DHOs obtained is greater than the number of pairwise non-isotopic presemifields used.