  A relationship between nilpotency and primeness in a module is investigated.
Reduced modules are expressed as sums of prime modules. It is shown that
presence of nilpotent module elements inhibits a module from possessing good
structural properties.
  A general form is given of an example used in literature to distinguish: 1)
completely prime modules from prime modules, 2) classical prime modules from
classical completely prime modules, and 3) a module which satisfies the
complete radical formula from one which is neither 2-primal nor satisfies the
radical formula.
