theorem Th34: :: IDEAL_2:30

for A being non degenerated commutative Ring
for I being Ideal of A holds
( I <> [#] A & ( for x, y being Element of A st x * y in I & not x in I holds
y in sqrt I ) iff ( not A / I is degenerated & ( for z being Element of (A / I) st z is zero_divisible holds
z is nilpotent ) ) )