Find all the radical of the commutative ring $Z_8$.
My book gives the following definition of the radical of a ring: "For a ring $R$, the radical is the set nilpotent elements." Is this standard terminology? However, when I came across this, which is defined similarly but goes by a different name. Is my book using standard terminology? If not, what is the standard terminology?
In Atiyah & Macdonald's An Introduction to Commutative Algebra they define the nilradical of a ring to be "the set...of all nilpotent elements in the ring" (chapter 1, page 5). I would say this is the more standard terminology.