4 problems

Wolffhardt's conjecture. If $\operatorname{Sym}_R(M)$ is a $\operatorname{UFD}$, then

Compressed-graph invariance conjecture. Under these hypotheses,

Compressed-graph structure conjecture. An edge joins the vertices represented by $\"]\phi(\prod_i d_i)$ and $\"]\phi(\prod_i b_i)$ if and only if

GCD-representative conjecture. For every $a\in D$,