Referring to Exercise 30, show that if N is the nilradical of a commutative ring R, then
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Referring to Exercise 30, show that if N is the nilradical of a commutative ring R, then R/N has as nilradical the trivial ideal {0 + N}.
Data from Exercise 30
An element a of a ring R is nilpotent if an= 0 for some n ∈ Z+. Show that the collection of all nilpotent elements in a commutative ring R is an ideal, the nilradical of R.
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