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Answer to Question #22749 in Algebra for Tsit Lam

Question #22749
Show that:any commutative ring is a quotient of a commutative rad-nil ring.
Expert's answer
For any commutative ring A,let R = A[t]. By Snapper’s Theorem rad(R) = rad (A[t]) =(Nil R)[t] = Nil (A[t]), so R is a rad-nil ring, and we have A ∼ R/(t).

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