微分大域
Differentially Large Fields
AI总结：
本文引入微分大域概念，建立其基础理论，给出多种刻画与构造，证明其初等性及在代数扩张下的保持性，表明其在微分域算术中的关键作用。
摘要：
我们引入了配备多个交换导子的域的微分大域概念（作为域的大域概念的类比）。我们为这一新的“驯服”微分域类奠定了基础。我们陈述了若干刻画，并展示了大量例子和应用。我们的结果强烈表明，微分大域将在微分域算术中发挥关键作用。例如，我们通过在其幂级数域（配备自然导子）中存在闭包来刻画微分大域，我们给出了基于迭代幂级数的微分大域的显式构造，我们证明了微分大域类是初等的，并且我们展示了微分大域在代数扩张下保持不变，从而表明其代数闭包是微分闭的。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
