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Dual of $Hom_A$End_A(M,M)$

Let $A$ be a finitely generated $\mathbb C$-algebra and an integral domain. Assume also $A$ is Gorenstein. Let $M$ be a finitely generated torsion-free $A$ module. Is it true that $Hom_A(Hom_A(M,M), A)\cong Hom_A(M,M)$$Hom_A(End_A(M), A)\cong End_A(M)$?

Dual of $Hom_A(M,M)$

Let $A$ be a finitely generated $\mathbb C$-algebra and an integral domain. Assume also $A$ is Gorenstein. Let $M$ be a finitely generated torsion-free $A$ module. Is it true that $Hom_A(Hom_A(M,M), A)\cong Hom_A(M,M)$?

Dual of $End_A(M)$

Let $A$ be a finitely generated $\mathbb C$-algebra and an integral domain. Assume also $A$ is Gorenstein. Let $M$ be a finitely generated torsion-free $A$ module. Is it true that $Hom_A(End_A(M), A)\cong End_A(M)$?

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user149914
user149914

Let $A$ be a finitely generated $\mathbb C$-algebra and an integral domain. Assume also $A$ is Gorenstein. Let $M$ be a finitely generated torsion-free $A$ module. Is it true that $Hom_A(Hom_A(M,M), A)=Hom_A(M,M)$$Hom_A(Hom_A(M,M), A)\cong Hom_A(M,M)$?

Let $A$ be a finitely generated $\mathbb C$-algebra and an integral domain. Assume also $A$ is Gorenstein. Let $M$ be a finitely generated torsion-free $A$ module. Is it true that $Hom_A(Hom_A(M,M), A)=Hom_A(M,M)$?

Let $A$ be a finitely generated $\mathbb C$-algebra and an integral domain. Assume also $A$ is Gorenstein. Let $M$ be a finitely generated torsion-free $A$ module. Is it true that $Hom_A(Hom_A(M,M), A)\cong Hom_A(M,M)$?

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user149914
user149914

Dual of $Hom_A(M,M)$

Let $A$ be a finitely generated $\mathbb C$-algebra and an integral domain. Assume also $A$ is Gorenstein. Let $M$ be a finitely generated torsion-free $A$ module. Is it true that $Hom_A(Hom_A(M,M), A)=Hom_A(M,M)$?