[代數] degree function
Let R be a Eucildean domain with degree fucntion P, and assume that b in R
is neither zero nor a unit.Prove that for every i≧0, P(b^i)<P(b^{i+1}).
我先用degree function 的定義寫下了
P(b^i)≦P(b^i*b)=P(b^{i+1})
然後用提示寫下了
exists q,r in R such that
b^i=b^{i+1}*q+r with P(r)<P(b^{i+1})
然後就束手無策了
感覺只差臨門一腳有誰可以幫我一下嗎?
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