LetR={

a b

0a|a,b∈ Z}

��ThenRis a ring with unity. Show that

P={

0b

0 0|b∈ Z}

is a prime ideal which is not maximal. Carefully justify all your claims.[Hint:Use the mapping ψ :R→ Z given by

ψ{

a b0a}

=a.]

a b

0 a are all matrices