The Cohen–Macaulayness of Direct Summands Conjecture

Let $A \rightarrow R$ be a ring homomorphism such that $A$ is a direct summand of $R$, and suppose that $R$ is regular. Cohen–Macaulayness of Direct Summands conjecture. Then $A$ is Cohen–Macaulay. This is one of the homological conjectures discussed in the source, concerning whether direct summands of regular rings inherit Cohen–Macaulayness. Its resolution status is not specified in the supplied source.