2 problems

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Faith's conjecture on left self-injective perfect rings
Faith's conjecture. Every left or right perfect, left self-injective ring is quasi-Frobenius.
Conjectureopenquasi-frobenius-rings ring-theory self-injective-ringsarXiv posted 2 days ago
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Extension of the self-injectivity theorem to $R_0=\mathbb{Z}_p$
Extension conjecture. The theorem remains true when $R_0$ is allowed to be $\mathbb{Z}_p$ .
Conjectureopencommutative-algebra graded-rings self-injective-ringsarXiv posted 2 days ago

Faith's conjecture on left self-injective perfect rings