Advanced galois theory/field theory book suggestions The Next CEO of Stack OverflowGood book resources (not websites) to learn number theory on my own?Tips for finding the Galois Group of a given polynomialSelf teaching Galois TheoryPrerequisites for Differential Galois theoryBook for field and galois theory.Challenging problems in algebra (book recommendation)Self-studying Information GeometryReference request for Galois TheoryRequesting material on Galois theoryBackground to start Galois theory
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Advanced galois theory/field theory book suggestions
The Next CEO of Stack OverflowGood book resources (not websites) to learn number theory on my own?Tips for finding the Galois Group of a given polynomialSelf teaching Galois TheoryPrerequisites for Differential Galois theoryBook for field and galois theory.Challenging problems in algebra (book recommendation)Self-studying Information GeometryReference request for Galois TheoryRequesting material on Galois theoryBackground to start Galois theory
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I have done the equivalent of an undergraduate algebra course(rings/fields/groups) and have read Stewart's Galois theory book. Galois theory was a lot of fun and I would like to continue studying it but I have no idea how to progress studying it or what the big theorems/questions further are.
I would like any suggestions on books that extend basic galois theory. All the suggestions I can find are at the level of Stewart's book(ie. end with essentially a proof of the insolubility of the quintic).
abstract-algebra galois-theory book-recommendation
asked Jun 11 '14 at 23:09
AsvinAsvin
3,44821432
$endgroup$
add a comment |
$begingroup$
I have done the equivalent of an undergraduate algebra course(rings/fields/groups) and have read Stewart's Galois theory book. Galois theory was a lot of fun and I would like to continue studying it but I have no idea how to progress studying it or what the big theorems/questions further are.
I would like any suggestions on books that extend basic galois theory. All the suggestions I can find are at the level of Stewart's book(ie. end with essentially a proof of the insolubility of the quintic).
abstract-algebra galois-theory book-recommendation
asked Jun 11 '14 at 23:09
AsvinAsvin
3,44821432
$endgroup$
2
$begingroup$
There is some deeper Galois theory in Isaac's Algebra. His treatment culminates in the Artin-Schrier theorem, which says that when the algebraic closure of a field is a finite degree extension, then it is very similar to the extension $|C:R|$. Another neat topic Galois theoretic topic is Hilbert's ramification theory, which you can find treated in the first (extremely dense) chapter of Neukirch's Algebraic Number Theory. I would recommend reading the sections on Galois theory and commutative algebra in Isaac's before reading Neukirch, since some of the basic exposition in Neukirch is lacking.
$endgroup$
– Lorenzo
Jun 12 '14 at 0:04
2
$begingroup$
Galois theory is a major underpinning of algebraic number theory as a whole, so you might like to go on to see a broader slice of that subject. I recommend all of J.S. Milne's course notes for number theory and algebraic geometry from the level you're already at through topics like etale cohomology that are rarely lectured.
$endgroup$
– Kevin Carlson
Jun 12 '14 at 0:08
add a comment |
$begingroup$
I have done the equivalent of an undergraduate algebra course(rings/fields/groups) and have read Stewart's Galois theory book. Galois theory was a lot of fun and I would like to continue studying it but I have no idea how to progress studying it or what the big theorems/questions further are.
I would like any suggestions on books that extend basic galois theory. All the suggestions I can find are at the level of Stewart's book(ie. end with essentially a proof of the insolubility of the quintic).
abstract-algebra galois-theory book-recommendation
asked Jun 11 '14 at 23:09
AsvinAsvin
3,44821432
$endgroup$
I have done the equivalent of an undergraduate algebra course(rings/fields/groups) and have read Stewart's Galois theory book. Galois theory was a lot of fun and I would like to continue studying it but I have no idea how to progress studying it or what the big theorems/questions further are.
I would like any suggestions on books that extend basic galois theory. All the suggestions I can find are at the level of Stewart's book(ie. end with essentially a proof of the insolubility of the quintic).
abstract-algebra galois-theory book-recommendation
abstract-algebra galois-theory book-recommendation
asked Jun 11 '14 at 23:09
AsvinAsvin
3,44821432
asked Jun 11 '14 at 23:09
AsvinAsvin
3,44821432
asked Jun 11 '14 at 23:09
AsvinAsvin
3,44821432
asked Jun 11 '14 at 23:09
AsvinAsvin
3,44821432
asked Jun 11 '14 at 23:09
AsvinAsvin
3,44821432
3,44821432
2
$begingroup$
There is some deeper Galois theory in Isaac's Algebra. His treatment culminates in the Artin-Schrier theorem, which says that when the algebraic closure of a field is a finite degree extension, then it is very similar to the extension $|C:R|$. Another neat topic Galois theoretic topic is Hilbert's ramification theory, which you can find treated in the first (extremely dense) chapter of Neukirch's Algebraic Number Theory. I would recommend reading the sections on Galois theory and commutative algebra in Isaac's before reading Neukirch, since some of the basic exposition in Neukirch is lacking.
$endgroup$
– Lorenzo
Jun 12 '14 at 0:04
2
$begingroup$
Galois theory is a major underpinning of algebraic number theory as a whole, so you might like to go on to see a broader slice of that subject. I recommend all of J.S. Milne's course notes for number theory and algebraic geometry from the level you're already at through topics like etale cohomology that are rarely lectured.
$endgroup$
– Kevin Carlson
Jun 12 '14 at 0:08
add a comment |
2
$begingroup$
There is some deeper Galois theory in Isaac's Algebra. His treatment culminates in the Artin-Schrier theorem, which says that when the algebraic closure of a field is a finite degree extension, then it is very similar to the extension $|C:R|$. Another neat topic Galois theoretic topic is Hilbert's ramification theory, which you can find treated in the first (extremely dense) chapter of Neukirch's Algebraic Number Theory. I would recommend reading the sections on Galois theory and commutative algebra in Isaac's before reading Neukirch, since some of the basic exposition in Neukirch is lacking.
$endgroup$
– Lorenzo
Jun 12 '14 at 0:04
2
$begingroup$
Galois theory is a major underpinning of algebraic number theory as a whole, so you might like to go on to see a broader slice of that subject. I recommend all of J.S. Milne's course notes for number theory and algebraic geometry from the level you're already at through topics like etale cohomology that are rarely lectured.
$endgroup$
– Kevin Carlson
Jun 12 '14 at 0:08
2
2
$begingroup$
There is some deeper Galois theory in Isaac's Algebra. His treatment culminates in the Artin-Schrier theorem, which says that when the algebraic closure of a field is a finite degree extension, then it is very similar to the extension $|C:R|$. Another neat topic Galois theoretic topic is Hilbert's ramification theory, which you can find treated in the first (extremely dense) chapter of Neukirch's Algebraic Number Theory. I would recommend reading the sections on Galois theory and commutative algebra in Isaac's before reading Neukirch, since some of the basic exposition in Neukirch is lacking.
$endgroup$
– Lorenzo
Jun 12 '14 at 0:04
$begingroup$
There is some deeper Galois theory in Isaac's Algebra. His treatment culminates in the Artin-Schrier theorem, which says that when the algebraic closure of a field is a finite degree extension, then it is very similar to the extension $|C:R|$. Another neat topic Galois theoretic topic is Hilbert's ramification theory, which you can find treated in the first (extremely dense) chapter of Neukirch's Algebraic Number Theory. I would recommend reading the sections on Galois theory and commutative algebra in Isaac's before reading Neukirch, since some of the basic exposition in Neukirch is lacking.
$endgroup$
– Lorenzo
Jun 12 '14 at 0:04
2
2
$begingroup$
Galois theory is a major underpinning of algebraic number theory as a whole, so you might like to go on to see a broader slice of that subject. I recommend all of J.S. Milne's course notes for number theory and algebraic geometry from the level you're already at through topics like etale cohomology that are rarely lectured.
$endgroup$
– Kevin Carlson
Jun 12 '14 at 0:08
$begingroup$
Galois theory is a major underpinning of algebraic number theory as a whole, so you might like to go on to see a broader slice of that subject. I recommend all of J.S. Milne's course notes for number theory and algebraic geometry from the level you're already at through topics like etale cohomology that are rarely lectured.
$endgroup$
– Kevin Carlson
Jun 12 '14 at 0:08
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
You can try Theory of Commutative Fields By M. Nagata
$endgroup$
add a comment |
$begingroup$
Galois groups are precisely the profinite groups. I recommend giving Wilson's book on profinite groups a look, and slowly you can make your way to reading Serre's Galois Cohomology.
answered Mar 18 at 12:06
MariahMariah
2,1431718
$endgroup$
$begingroup$
just noticed this is a very old question ha..
$endgroup$
– Mariah
Mar 18 at 12:08
add a comment |
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2 Answers
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2 Answers
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$begingroup$
You can try Theory of Commutative Fields By M. Nagata
$endgroup$
add a comment |
$begingroup$
You can try Theory of Commutative Fields By M. Nagata
$endgroup$
add a comment |
$begingroup$
You can try Theory of Commutative Fields By M. Nagata
$endgroup$
You can try Theory of Commutative Fields By M. Nagata
answered Mar 29 '17 at 18:01
user379195
add a comment |
add a comment |
$begingroup$
Galois groups are precisely the profinite groups. I recommend giving Wilson's book on profinite groups a look, and slowly you can make your way to reading Serre's Galois Cohomology.
answered Mar 18 at 12:06
MariahMariah
2,1431718
$endgroup$
$begingroup$
just noticed this is a very old question ha..
$endgroup$
– Mariah
Mar 18 at 12:08
add a comment |
$begingroup$
Galois groups are precisely the profinite groups. I recommend giving Wilson's book on profinite groups a look, and slowly you can make your way to reading Serre's Galois Cohomology.
answered Mar 18 at 12:06
MariahMariah
2,1431718
$endgroup$
$begingroup$
just noticed this is a very old question ha..
$endgroup$
– Mariah
Mar 18 at 12:08
add a comment |
$begingroup$
Galois groups are precisely the profinite groups. I recommend giving Wilson's book on profinite groups a look, and slowly you can make your way to reading Serre's Galois Cohomology.
answered Mar 18 at 12:06
MariahMariah
2,1431718
$endgroup$
Galois groups are precisely the profinite groups. I recommend giving Wilson's book on profinite groups a look, and slowly you can make your way to reading Serre's Galois Cohomology.
answered Mar 18 at 12:06
MariahMariah
2,1431718
answered Mar 18 at 12:06
MariahMariah
2,1431718
answered Mar 18 at 12:06
MariahMariah
2,1431718
answered Mar 18 at 12:06
MariahMariah
2,1431718
2,1431718
$begingroup$
just noticed this is a very old question ha..
$endgroup$
– Mariah
Mar 18 at 12:08
add a comment |
$begingroup$
just noticed this is a very old question ha..
$endgroup$
– Mariah
Mar 18 at 12:08
$begingroup$
just noticed this is a very old question ha..
$endgroup$
– Mariah
Mar 18 at 12:08
$begingroup$
just noticed this is a very old question ha..
$endgroup$
– Mariah
Mar 18 at 12:08
add a comment |
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There is some deeper Galois theory in Isaac's Algebra. His treatment culminates in the Artin-Schrier theorem, which says that when the algebraic closure of a field is a finite degree extension, then it is very similar to the extension $|C:R|$. Another neat topic Galois theoretic topic is Hilbert's ramification theory, which you can find treated in the first (extremely dense) chapter of Neukirch's Algebraic Number Theory. I would recommend reading the sections on Galois theory and commutative algebra in Isaac's before reading Neukirch, since some of the basic exposition in Neukirch is lacking.
$endgroup$
– Lorenzo
Jun 12 '14 at 0:04
2
$begingroup$
Galois theory is a major underpinning of algebraic number theory as a whole, so you might like to go on to see a broader slice of that subject. I recommend all of J.S. Milne's course notes for number theory and algebraic geometry from the level you're already at through topics like etale cohomology that are rarely lectured.
$endgroup$
– Kevin Carlson
Jun 12 '14 at 0:08