In [1], D. Daigle has proved a few results on “tameness” of a degree function on an integral domain B containing $\mathbb{Q}$, which ensure that, under certain hypotheses, a derivation on B gives rise to a homogeneous derivation on an associated graded ring of B induced by the degree function.

In this paper, we extend Daigle's results to arbitrary integral domains not necessarily containing $\mathbb{Q}$.

中文翻译：

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驯服度函数具有任意特征

在[1]，D英对照精华文章已经证明上的程度的函数“温顺”几个结果上的积分域乙含$\mathbb{问}$，这确保了在某些假设下，对B的导数会在由度函数引起的B的相关渐变环上引起同质导数。

在本文中，我们将Daigle的结果扩展到不一定包含的任意整数域 $\mathbb{问}$。