Show that:any commutative ring is a quotient of a commutative rad-nil ring.
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Expert's answer
2013-01-31T08:01:21-0500
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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