3. Examples
Last lecture we defined what it means that a polynomial with coefficients in a field is solvable by radicals over . Namely, there is a tower of extensions
where for each there is a positive integer such that and such that
3. Examples
Last lecture we defined what it means that a polynomial with coefficients in a field is solvable by radicals over . Namely, there is a tower of extensions
where for each there is a positive integer such that and such that
1 Comment | 305: Abstract Algebra I | Tagged: cubic equation, extension by radicals, quartic equation | Permalink
Posted by andrescaicedo
2. Extensions by radicals
Last lecture we defined where is a subfield of a field all the roots of the polynomial are in and all the coefficients of are in Namely, if are the roots of then the field generated by over
The typical examples we will consider are those where and the coefficients of are rational or in fact, integers.
2 Comments | 305: Abstract Algebra I | Tagged: extension by radicals, extension field, ring | Permalink
Posted by andrescaicedo
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