# 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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