for some and units it's clear now that if then and if then it's now obvious that is indecomposable because if for some submoules
then we'll have but, as we just showed either or so we must have either or
suppose has at least two distinct prime factors. let be a prime factor of so we have where therefore see that and so(ii) Let R be a PID and d is non_zero, non_unit. If R/(d) is indecomposable, show that d~p^n for some prime p in R.
Can you give me some hints how to do this question please?
Thank you so much
which contradicts indecomposablity of thus is the only prime factor of and hence and are associates.