Differential Galois theory III: Some inverse problems
Differential Galois theory III: Some inverse problems
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微分伽罗瓦理论 III：一些反问题
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
A. Pillay
中科院分区：
文献类型：
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作者：
D. Marker;A. Pillay
在[16]中，发展了微分场的广义强正规扩张理论，推广了Kolchin的理论[8]。证明了任意有限维微分代数群都可以作为微分伽罗瓦群出现。事实上，我们的理论是一个适当的概括Kolchin的正是由于存在有限维微分代数群不同构代数群的常数。在本文中，我们开始研究广义强正规扩张的反问题。我们以后称广义强正规扩张为微分伽罗瓦扩张。我们不妨开始陈述一个一般性的猜想，其中的记号将在后面解释。
In 16], a theory of generalised strongly normal extensions of differential fields was developed, generalising Kolchin’s theory [8]. It was shown that arbitrary finitedimensional differential algebraic groups can arise as differential Galois groups for this new theory. The fact that our theory is a proper generalisation of Kolchin’s is due precisely to the existence of finite-dimensional differential algebraic groups which are not isomorphic to algebraic groups in the constants. In this paper we initiate a study of the inverse problem for generalised strongly normal extensions. We will henceforth call generalised strongly normal extensions, differential Galois extensions. We may as well begin by stating a general conjecture, where notation will be explained subsequently.