Monday, 22 December 2014

abstract algebra - (McapE)(McapF)=M for linearly disjoint fields E and F?



Let E and F be linearly disjoint fields over a base field K (all contained in an algebraic closure ¯K). Suppose there is an extension M/K contained in EF.
Is it true that (ME)(MF)=M?
I was not able to show it. Does anybode have an idea?


Answer



It is not true, see mihaild's comment.


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