Where I could see the following statement?

Let $K\subset L\subset M$ be a tower of the strongly normal extensions of differential fields. If $M$ is weakly normal over $K$, then $M$ is strongly normal over $K$.


It is not true. See the example in my paper Algebraic D-groups and differential galois theory, Pacific Journal Math, vol 216, No. 2, 2004. It is discussed on p. 356.

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  • $\begingroup$ Thank you for counterexample professor Pillay. I have read the above statement many years ago and do not remember where. So, apparently, I missed some important condition of context. Maybe $K$ must be finitely generated and finite transcendence degree over the constants. $\endgroup$ – user75594 Jul 1 '15 at 17:31

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