On some open problems in commutative algebra resolved by Rethlas

We report on a collection of open problems in commutative algebra and related areas that have been resolved (proved or disproved) using the Rethlas natural-language automated reasoning system. The problems are drawn from several published lists, including Open Problems in Commutative Ring Theory (Cahen-Fontana-Frisch-Glaz), Eisenbud-Schreyer's survey of Boij-S\"oderberg theory. For each problem we record the precise statement and a self-contained proof produced (with no human intervention) by Rethlas and subsequently verified by human experts.