Wednesday, June 13, 2018

abstract algebra - Degree of a finite field extension. How to find?




What is the degree of the extension [Q(2+3+5):Q]?
Can you explain, what I must to do in this example?


Answer



[Q(2+3+5):Q]=[Q(2,3,5):Q]=[Q(2,3,5):Q(2,3)].[Q(2,3):Q(2)].[Q(2):Q]=2.2.2=8




Q(2+3+5) is a 8 degree extension over Q.And basis are 1,2,3,5,6,10,15,30


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