Question #25251

Show that from if I is a nil ideal in any ring R, then I[t] ⊆ rad R[t], follows rad (R[t]) = (Nil*R)[t] for any ring R.

Expert's answer

The inclusion “*⊆*” in conclusion follows fromAmitsur’s Theorem. The reverse inclusion “*⊇*” follows from given assumption: "* I*[*t*]*⊆*rad *R*[*t*], for *I *is a nil ideal ".So, rad (*R*[*t*]) = (Nil**R*)[*t*].

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