6 problems

Let $S=k[x_1,\ldots,x_n]$, let $\mathfrak a=\langle m_1,\ldots,m_l\rangle\subset S$ be a monomial ideal, and set $A=S/\mathfrak a$. The ideal $\mathfrak a$ satisfies the strong gcd…

Let $I$ be a symmetric monomial ideal, and suppose that the conditions in Theorem 1 hold: for every $2\leq p\leq n$, either all relevant partitions of length at most…

Let $(R,\mathfrak{m},k)$ be a local Golod ring of embedding codimension $e$. An indecomposable-syzygy conjecture asserts that there is a set of at most $e+1$ indecomposable $R$-mod…

Let $Q$ be a standard graded polynomial ring over a field, let $R$ be a graded quotient of $Q$, and suppose that its Tor algebra has the form … where $\mathsf{P}$ is a graded algeb…

Golod–co-$H$-space conjecture. The complex $K$ is Golod if and only if $\mathcal Z_K$ is a co-$H$-space.

Let $\Delta$ be a simplicial complex. Its strong gcd-condition means that its minimal non-faces admit a strong gcd-order: a linear order $M_1,\ldots,M_r$ such that whenever…