Question: Let R be a ring. (a) Show that nil(R) is an ideal of R. (b) Show that nil( Ril(R)) = 0. Definition. Let R be

Let R be a ring. (a) Show that nil(R) is an ideal of R. (b) Show that nil( Ril(R)) = 0. Definition. Let R be a ring. An element x of R is called nilpotent iff there exists m E N such that xm = 0 in R. The set nil(R) := {xER : x is nilpotent} is called the nilradical of R

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