作者jacky7987 (忆)
看板Math
标题[代数] degree function
时间Tue Mar 22 00:37:01 2011
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 的定义写下了
P(b^i)≦P(b^i*b)=P(b^{i+1})
然後用提示写下了
exists q,r in R such that
b^i=b^{i+1}*q+r with P(r)<P(b^{i+1})
然後就束手无策了
感觉只差临门一脚有谁可以帮我一下吗?
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1F：推 yusd24 :因为 b 不是 unit 03/22 09:06
2F：推 LimSinE :移项 03/22 09:22
3F：→ jacky7987 :不好意思还是不甚了解可以说得清楚一点吗,谢谢 03/22 22:34