4 problems

Let $A$ be an Artin algebra. Its left and right self-injective dimensions are the injective dimensions of the regular module on the left and right, respectively. Gorenstein symmetr…

Gorenstein bimodule conjecture. $A$ is self-injective if and only if $A$, regarded as an $A$-bimodule, is Gorenstein-projective.

Let $\Lambda$ be an artin algebra, and let … be a minimal injective resolution of the left $\Lambda$-module $\Lambda$. Auslander–Gorenstein conjecture. If…

Equality conjecture. For any ring $R$,