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first of all, that should beOriginally Posted by Erdos32212
Supposeis a ring and
are relatively prime ideals of
. Prove that for any integers
,
.
and also i assume that your ring is commutative with unity. so you only need to show that
this is very easy:
sincethere exist
such that
thus:
^{m+n}=r^n \sum_{i=0}^m \binom{n+m}{i}r^{m-i}s^i \ + \ s^m \sum_{i=m+1}^{n+m} \binom{n+m}{i}r^{n+m-i}s^{i-m} \in I^n + J^m. \ \Box)
