SOLUTION: Show that I= (2,t)= {g(t)*2 + h(t)*t : g(t),h(t) belongs Z[t]} is a non-principal ideal in Z[t]. note: Z stands for Intergers

SOLUTION: Show that I= (2,t)= {g(t)2 + h(t)t : g(t),h(t) belongs Z[t]} is a non-principal ideal in Z[t]. note: Z stands for Intergers

Question 31159: Show that I= (2,t)= {g(t)*2 + h(t)*t : g(t),h(t) belongs Z[t]} is a non-principal ideal in Z[t].
note: Z stands for Intergers
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
1) Show that I=(2,t) = {g(t)*2 + h(t)*t : g(t), h(t) belongs to Z[t]} is a
> non principal ideal in Z[t].
> Z meaning integers
> DO YOU MEAN (2,T) IS THE GENERATOR TO BE TESTED?IF SO
WE HAVE I = SAY FOR G(T)=1 AND H(T)=3....
I=(2,3T)...WHICH CANNOT BE GENERATED BY (2,T)..SINCE THERE IS NO A AN
INTEGER WHICH GIVES
A(2,T)=(2,3T)
HENCE I IS NOT A PRINCIPAL IDEAL.
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