论文标题
差异很大
Differentially Large Fields
论文作者
论文摘要
我们介绍了配备多个通勤派生的田野的差异宽敞概念（作为对田地宽敞的类似）。我们列出了这一新类“ Tame”差异字段的基础。我们陈述了几种特征，并展示了许多例子和应用。我们的结果强烈表明，差异性较大的场将在差异场算术中起关键作用。例如，我们在其功率系列字段（以自然推导的功能）中的生存封闭来表征差异性的差异，从迭代的力量系列中，我们给出了差异性较大领域的明确结构，我们证明了一类差分较大的领域是基本的，我们证明了差异性宽敞的范围在代数的范围内保留了差异，因此差异化了它们的差异，从而差异化。
We introduce the notion of differential largeness for fields equipped with several commuting derivations (as an analogue to largeness of fields). We lay out the foundations of this new class of "tame" differential fields. We state several characterizations and exhibit plenty of examples and applications. Our results strongly indicate that differentially large fields will play a key role in differential field arithmetic. For instance, we characterise differential largeness in terms of being existentially closed in their power series field (furnished with natural derivations), we give explicit constructions of differentially large fields in terms of iterated powers series, we prove that the class of differentially large fields is elementary, and we show that differential largeness is preserved under algebraic extensions, therefore showing that their algebraic closure is differentially closed.
