(1a) Note that if is prime then .
(1b) You can show this by induction on .
(2) . Show that is not a unit of and in .
(1)
Given Integral domain R and
a) not unit, is called prime element
if a|bc implies a|b or a|c.
Show that a is prime element iff <a> is prime ideal
b) not unit, is said un-reduced
if a = bc implies b is unit or c is unit.
Show that if p is prime and for some i.
(2)
If . What criteria must be held by ? (is it prime or un-reduced?)