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Answer by user26857 for Is a surjective $R$-endomorphism over a finitely...

Let $A$ be a commutative ring, and $R$ a finitely generated $A$-algebra. Then every surjective $A$-endomorphism of $R$ is injective.Let $f:R\to R$ be a surjective $A$-endomorphism, and $0 \neq x_0 \in...

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Is a surjective $R$-endomorphism over a finitely generated $R$ algebra always...

Let $R$ be a unital commutative ring and $A$ a finitely generated $R$-algebra. I found out that if $R$ is a field, then any surjective $R$-endomorphism over $A$ must be injective, too. Does that hold...

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