Characterizing Cohen-Macaulay local rings by Frobenius maps
Characterizing Cohen-Macaulay local rings by Frobenius maps
Let $R$ be a commutative noetherian local ring of prime characteristic. Denote by ${{}^e\hspace {-1.6pt}{}} R$ the ring $R$ regarded as an $R$-algebra through $e$-times composition of the Frobenius map. Suppose that $R$ is F-finite, i.e., ${{}^1\hspace {-2pt}{}} R$ is a finitely generated $R$-module. We prove that $R$ is Cohen-Macaulay …