Given the following polynomials 1) X^2-2 belongs to Q[X]


                                2) X^4-5 belongs to Q[X]


                                3) (X^3-2)(X^2-3) belongs to Q[X]

 1) Find a basis for the splitting field over the filed Q
 2) the degree of the splitting field over Q
 3) determine the Galois group of the polynomial over Q.

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Request for Question Clarification by mathtalk-ga on 04 May 2004 05:34 PDT

Hi, vascucat-ga:

I thought at first glance that your Question referred to a minimal
field in which all three polynomials would split, but on reflection it
seems more likely that there are three splitting fields/subproblems in
your request, one for each of the three polynomials described under
1),2),3) in the first portion of your Question.

Would you confirm that for _each_ of these three example polynomials
you would like Answers to points 1),2),3) in the bottom portion of the
Question?

thanks in advance,
mathtalk-ga

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Clarification of Question by vasucat-ga on 04 May 2004 21:55 PDT

hi mathtalk-ga,

  yes for the given three example polynomials I want the answers for
the points 1),2),3) in the bottom portion of the
Question. 

  If you have any problem then please ask me I will clarify the question.

 hoping to hear from you soon.

 thanks,
vasucat-ga.

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Clarification of Question by vasucat-ga on 04 May 2004 22:06 PDT

A) Given the polynomial X^2-2 belongs to  Q[x], 
  calculate
 (i) a basis for the splitting field over the field over Q,
 (ii) the degree of the splitting field over Q, 
 (iii) determine the Galois group of the polynomial over Q.

B)Given the polynomial X^4-5 belongs to  Q[x]
  calculate
 (i) a basis for the splitting field over the field over Q,
 (ii) the degree of the splitting field over Q, 
 (iii) determine the Galois group of the polynomial over Q.

C) Given the polynomial (X^3-2)(X^2-3) belongs to  Q[x]
  calculate
 (i)   a basis for the splitting field over the field over Q,
 (ii)  the degree of the splitting field over Q, 
 (iii) determine the Galois group of the polynomial over Q.

 
  in the above problems X^ means X square.

 i hope it is clear now. waiting for your answer


 thanks,
vasucat-ga

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Request for Question Clarification by mathtalk-ga on 06 May 2004 08:02 PDT

Hi, vasucat-ga:

Please see the other Question of this type you posted, where I've
requested a clarification of you background (so as to be able to pitch
the explanation at an appropriate level).

thanks, mathtalk-ga