let R be ring
definition of semiprime ring:
R is semiprime if aRa=0 implies a=0
definition of prime ring:
R is prime if aRb=0 implies a=0 or b=0
from that definition i think semiprime wider than prime (like semiring and ring) thus any prime is semiprime. <== is this true?
if that true, is there any example of semiprime but not prime?