Galois Theory and AR Theorem Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Questions about the details of Abel's theoremGalois Theory and Galois GroupsHow does trigonometry in a Galois field work?Precise meaning of “Solution in radicals”Galois group of the field of all constructible complex numbersUnsolvability of a Quintic and its link with “Simplicity” of $A_5$Solvable but not radical.Does there always exist an automorphism in $Gal(E/ℚ(x_1))$ besides the indentity?The Galois group seen abstractly for a field extension, and for a concrete polynomialAlgebraic numbers expressible in terms of real-valued radicals
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Galois Theory and AR Theorem
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Questions about the details of Abel's theoremGalois Theory and Galois GroupsHow does trigonometry in a Galois field work?Precise meaning of “Solution in radicals”Galois group of the field of all constructible complex numbersUnsolvability of a Quintic and its link with “Simplicity” of $A_5$Solvable but not radical.Does there always exist an automorphism in $Gal(E/ℚ(x_1))$ besides the indentity?The Galois group seen abstractly for a field extension, and for a concrete polynomialAlgebraic numbers expressible in terms of real-valued radicals
$begingroup$
I’m trying to understand the proof that there will never be a quintic formula. Some questions:
What is the name for a number which is formed from progressive radicals and algebraic operations, i.e. a number which could be described with a formula? Example $sqrtsqrt2+sqrt3$.
How do you prove that when you adjoin an element like this to the field, that that field extension contains the component radicals? For are example $sqrt2$ and $sqrt3$?
I have been trying to work this out for ages but not making much progress. Be gentle with me I dont have a maths degree.
abstract-algebra galois-theory
edited Mar 27 at 12:10
Shaun
10.7k113687
asked Mar 27 at 7:59
user157872user157872
263
$endgroup$
add a comment |
$begingroup$
I’m trying to understand the proof that there will never be a quintic formula. Some questions:
What is the name for a number which is formed from progressive radicals and algebraic operations, i.e. a number which could be described with a formula? Example $sqrtsqrt2+sqrt3$.
How do you prove that when you adjoin an element like this to the field, that that field extension contains the component radicals? For are example $sqrt2$ and $sqrt3$?
I have been trying to work this out for ages but not making much progress. Be gentle with me I dont have a maths degree.
abstract-algebra galois-theory
edited Mar 27 at 12:10
Shaun
10.7k113687
asked Mar 27 at 7:59
user157872user157872
263
$endgroup$
5
$begingroup$
1. You say this number is expressible by radicals. 2. In general this is very hard. See theorem 2.11 here
$endgroup$
– Wojowu
Mar 27 at 8:11
add a comment |
$begingroup$
I’m trying to understand the proof that there will never be a quintic formula. Some questions:
What is the name for a number which is formed from progressive radicals and algebraic operations, i.e. a number which could be described with a formula? Example $sqrtsqrt2+sqrt3$.
How do you prove that when you adjoin an element like this to the field, that that field extension contains the component radicals? For are example $sqrt2$ and $sqrt3$?
I have been trying to work this out for ages but not making much progress. Be gentle with me I dont have a maths degree.
abstract-algebra galois-theory
edited Mar 27 at 12:10
Shaun
10.7k113687
asked Mar 27 at 7:59
user157872user157872
263
$endgroup$
I’m trying to understand the proof that there will never be a quintic formula. Some questions:
What is the name for a number which is formed from progressive radicals and algebraic operations, i.e. a number which could be described with a formula? Example $sqrtsqrt2+sqrt3$.
How do you prove that when you adjoin an element like this to the field, that that field extension contains the component radicals? For are example $sqrt2$ and $sqrt3$?
I have been trying to work this out for ages but not making much progress. Be gentle with me I dont have a maths degree.
abstract-algebra galois-theory
abstract-algebra galois-theory
edited Mar 27 at 12:10
Shaun
10.7k113687
asked Mar 27 at 7:59
user157872user157872
263
edited Mar 27 at 12:10
Shaun
10.7k113687
asked Mar 27 at 7:59
user157872user157872
263
edited Mar 27 at 12:10
Shaun
10.7k113687
edited Mar 27 at 12:10
Shaun
10.7k113687
edited Mar 27 at 12:10
Shaun
10.7k113687
10.7k113687
asked Mar 27 at 7:59
user157872user157872
263
asked Mar 27 at 7:59
user157872user157872
263
asked Mar 27 at 7:59
user157872user157872
263
263
5
$begingroup$
1. You say this number is expressible by radicals. 2. In general this is very hard. See theorem 2.11 here
$endgroup$
– Wojowu
Mar 27 at 8:11
add a comment |
5
$begingroup$
1. You say this number is expressible by radicals. 2. In general this is very hard. See theorem 2.11 here
$endgroup$
– Wojowu
Mar 27 at 8:11
5
5
$begingroup$
1. You say this number is expressible by radicals. 2. In general this is very hard. See theorem 2.11 here
$endgroup$
– Wojowu
Mar 27 at 8:11
$begingroup$
1. You say this number is expressible by radicals. 2. In general this is very hard. See theorem 2.11 here
$endgroup$
– Wojowu
Mar 27 at 8:11
add a comment |
0
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$begingroup$
1. You say this number is expressible by radicals. 2. In general this is very hard. See theorem 2.11 here
$endgroup$
– Wojowu
Mar 27 at 8:11