6 problems

Conjecture. Under either of these hypotheses, $I_{\mathfrak{a}}(\mathbb{F})$ has the stated polynomial-algebra structure with the given derivation action.

Guo's conjecture. Every $R$-module has an $(R,S)$-injective envelope.

Compact-subgroup injectivity conjecture. If $\pi\in\mathfrak{Rep}^{\textnormal{ladm}}(G)$ is injective, then $\pi|_K$ is injective in $\mathfrak{Rep}^\infty(K)$. Consequently,

Il'in's conjecture. Every left (right) $S$-semimodule has an injective hull if and only if $S$ is additively regular. This conjecture characterizes semirings for which the category…

Let $R$ be a ring. A ring is right $R$-tight when every cyclic submodule of its injective envelope $E(R_R)$ embeds in $R$, and it is right PF when it is right self-injective and ri…

Local detection conjecture. Rational injectivity of $M$ should be detected by this local information; that is, the restrictions of $M$ to all Frobenius kernels, or equivalently its…