(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?)