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**laipou****Member**- Registered: 2009-09-19
- Posts: 24

(1)Is there exists a polynomial

such that its splitting field is contained in a radical extension over ,but is not radical over?(2)suppose .

What does "Solve for a by radicals" mean?

Thanks for any help.

*Last edited by laipou (2010-04-23 16:19:22)*

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**laipou****Member**- Registered: 2009-09-19
- Posts: 24

Sorry,the title should be "radical extension".

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

1. If F is a radical extension, then

What can you say about the intermediate fields in between F and Q?

2. "Solve by radicals" means come up with an expression for e^(2pi i)/7 using only rational numbers, addition, subtraction, multiplication, division, and (rational) exponents.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**laipou****Member**- Registered: 2009-09-19
- Posts: 24

All I know is that

is solvable for all intermediate field .Is this helpful?

*Last edited by laipou (2010-04-25 21:26:47)*

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Solvable won't do it for you. Think "Fundamental theorem of Galois theory".

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**laipou****Member**- Registered: 2009-09-19
- Posts: 24

I don't understand how "Fundamental theorem of Galois theory" works here.

Could you tell me more?

Thx.

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