9 problems

Let $K$ be a difference field and let $R$ be a finitely difference generated difference algebra over $K$. A difference ideal in $R$ is radical well-mixed if it is both radical and…

Let $L$ be a nonmodular lattice, and let $I_L$ denote its join–meet ideal. An ideal is linearly related when its linear syzygies generate all of its syzygies. Nonmodular-lattice jo…

Primality conjecture. The following conditions are equivalent:

Let $R$ be a difference polynomial ring, and let a binomial difference ideal be a difference ideal generated by binomials. Its radical well-mixed closure is the smallest radical we…

Graph-origin conjecture. The polyomino ideal $I_{\mathcal P}$ comes from a finite simple graph if and only if $\mathcal P$ is nonsimple.

Let $I$ be an ideal generated by binomials, and suppose that $I$ has a quadratic Gröbner basis with respect to every monomial order. Say that the generators of $I$ are in pairwise…

Let $\Bbbk$ be an algebraically closed field of arbitrary characteristic, let $Q$ be a finitely generated commutative monoid, and let $\Bbbk[Q]$ be its monoid algebra. Mesoprimary…

Let $E$ be a grid, and let $I^{E}$ denote its commuting birth and death ideal, formed as the sum of the ideals associated with all induced squares of $E$. Evans–Sturmfels–Uhler con…

Let $A$ be the localization of ${\mathbb{Z}}$ at a nonzero integer, let ${\mathfrak{a}}$ be a nonzero ideal of $A[x_1,\dots,x_n]$ contained in $(x_1,\dots,x_n)$, and let…