Earliest use of the term “Galois extension”? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)transcendental Galois theoryGalois theory timelineGalois theory timeline (II)An advanced exposition of Galois theoryHistory of the Normal Basis TheoremDecomposition group vs Galois group of completed extension for height > 1 primesWhen did the term “Lie group” first appear?why are subextensions of Galois extensions also Galois?When is a Fourier coefficient field Galois?Having a separable extension of degree $n$ implies having a Galois extension of degree $n$?
Multi tool use
Earliest use of the term “Galois extension”?
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)transcendental Galois theoryGalois theory timelineGalois theory timeline (II)An advanced exposition of Galois theoryHistory of the Normal Basis TheoremDecomposition group vs Galois group of completed extension for height > 1 primesWhen did the term “Lie group” first appear?why are subextensions of Galois extensions also Galois?When is a Fourier coefficient field Galois?Having a separable extension of degree $n$ implies having a Galois extension of degree $n$?
$begingroup$
Does anyone know the earliest use of the term "Galois extension"? I thought it might be in Emil Artin's Notre Dame lectures but I couldn't find it there. (He does use the terms "normal" and "separable.")
ho.history-overview galois-theory
asked Apr 10 at 14:04
Drew ArmstrongDrew Armstrong
1,555830
$endgroup$
add a comment |
$begingroup$
Does anyone know the earliest use of the term "Galois extension"? I thought it might be in Emil Artin's Notre Dame lectures but I couldn't find it there. (He does use the terms "normal" and "separable.")
ho.history-overview galois-theory
asked Apr 10 at 14:04
Drew ArmstrongDrew Armstrong
1,555830
$endgroup$
$begingroup$
The earliest occurrence in MathSciNet seems to be in the review of "Une généralisation de la notion de corps—corpoïde. Un corpoïde remarquable de la théorie des corps valués" by Marc Krasner, C. R. Acad. Sci. Paris 219, (1944) 345–347. The relevant sentence is "Commutative extension corpoids are discussed and Galois extensions defined."
$endgroup$
– Timothy Chow
Apr 11 at 2:49
add a comment |
$begingroup$
Does anyone know the earliest use of the term "Galois extension"? I thought it might be in Emil Artin's Notre Dame lectures but I couldn't find it there. (He does use the terms "normal" and "separable.")
ho.history-overview galois-theory
asked Apr 10 at 14:04
Drew ArmstrongDrew Armstrong
1,555830
$endgroup$
Does anyone know the earliest use of the term "Galois extension"? I thought it might be in Emil Artin's Notre Dame lectures but I couldn't find it there. (He does use the terms "normal" and "separable.")
ho.history-overview galois-theory
ho.history-overview galois-theory
asked Apr 10 at 14:04
Drew ArmstrongDrew Armstrong
1,555830
asked Apr 10 at 14:04
Drew ArmstrongDrew Armstrong
1,555830
asked Apr 10 at 14:04
Drew ArmstrongDrew Armstrong
1,555830
asked Apr 10 at 14:04
Drew ArmstrongDrew Armstrong
1,555830
asked Apr 10 at 14:04
Drew ArmstrongDrew Armstrong
1,555830
1,555830
$begingroup$
The earliest occurrence in MathSciNet seems to be in the review of "Une généralisation de la notion de corps—corpoïde. Un corpoïde remarquable de la théorie des corps valués" by Marc Krasner, C. R. Acad. Sci. Paris 219, (1944) 345–347. The relevant sentence is "Commutative extension corpoids are discussed and Galois extensions defined."
$endgroup$
– Timothy Chow
Apr 11 at 2:49
add a comment |
$begingroup$
The earliest occurrence in MathSciNet seems to be in the review of "Une généralisation de la notion de corps—corpoïde. Un corpoïde remarquable de la théorie des corps valués" by Marc Krasner, C. R. Acad. Sci. Paris 219, (1944) 345–347. The relevant sentence is "Commutative extension corpoids are discussed and Galois extensions defined."
$endgroup$
– Timothy Chow
Apr 11 at 2:49
$begingroup$
The earliest occurrence in MathSciNet seems to be in the review of "Une généralisation de la notion de corps—corpoïde. Un corpoïde remarquable de la théorie des corps valués" by Marc Krasner, C. R. Acad. Sci. Paris 219, (1944) 345–347. The relevant sentence is "Commutative extension corpoids are discussed and Galois extensions defined."
$endgroup$
– Timothy Chow
Apr 11 at 2:49
$begingroup$
The earliest occurrence in MathSciNet seems to be in the review of "Une généralisation de la notion de corps—corpoïde. Un corpoïde remarquable de la théorie des corps valués" by Marc Krasner, C. R. Acad. Sci. Paris 219, (1944) 345–347. The relevant sentence is "Commutative extension corpoids are discussed and Galois extensions defined."
$endgroup$
– Timothy Chow
Apr 11 at 2:49
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Not an answer, but an extended comment. Probably the terminology is not due to Artin. The Notre Dame lectures were in 1942 and published in 1944. In Emil Artin's 1947 lecture notes (notes taken by Albert A Blank, and seems to have been printed by Courant Institute; I'm not sure as I only have a photocopy) what normally is now called a Galois extension he calls a "normal extension" (he used normal differently from how it is used today).
This is also corroborated by a footnote in Hungerford's Algebra. In my edition the definition of a Galois extension (Definition 2.4 in Chapter V) has a footnote that reads (emphasis mine):
A Galois extension is frequently required to be finite dimensional or at least algebraic ... equivalent to the usual one. Our definition is essentially due to Artin, except that he calls such an extension "normal." Since this use of "normal" conflicts (in case char $Fneq 0$) with the definition of "normal" used by many other authors, we have chosen to follow Artin's basic approach, but to retain the (more or less) conventional terminology.
$endgroup$
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "504"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathoverflow.net%2fquestions%2f327674%2fearliest-use-of-the-term-galois-extension%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Not an answer, but an extended comment. Probably the terminology is not due to Artin. The Notre Dame lectures were in 1942 and published in 1944. In Emil Artin's 1947 lecture notes (notes taken by Albert A Blank, and seems to have been printed by Courant Institute; I'm not sure as I only have a photocopy) what normally is now called a Galois extension he calls a "normal extension" (he used normal differently from how it is used today).
This is also corroborated by a footnote in Hungerford's Algebra. In my edition the definition of a Galois extension (Definition 2.4 in Chapter V) has a footnote that reads (emphasis mine):
A Galois extension is frequently required to be finite dimensional or at least algebraic ... equivalent to the usual one. Our definition is essentially due to Artin, except that he calls such an extension "normal." Since this use of "normal" conflicts (in case char $Fneq 0$) with the definition of "normal" used by many other authors, we have chosen to follow Artin's basic approach, but to retain the (more or less) conventional terminology.
$endgroup$
add a comment |
$begingroup$
Not an answer, but an extended comment. Probably the terminology is not due to Artin. The Notre Dame lectures were in 1942 and published in 1944. In Emil Artin's 1947 lecture notes (notes taken by Albert A Blank, and seems to have been printed by Courant Institute; I'm not sure as I only have a photocopy) what normally is now called a Galois extension he calls a "normal extension" (he used normal differently from how it is used today).
This is also corroborated by a footnote in Hungerford's Algebra. In my edition the definition of a Galois extension (Definition 2.4 in Chapter V) has a footnote that reads (emphasis mine):
A Galois extension is frequently required to be finite dimensional or at least algebraic ... equivalent to the usual one. Our definition is essentially due to Artin, except that he calls such an extension "normal." Since this use of "normal" conflicts (in case char $Fneq 0$) with the definition of "normal" used by many other authors, we have chosen to follow Artin's basic approach, but to retain the (more or less) conventional terminology.
$endgroup$
add a comment |
$begingroup$
Not an answer, but an extended comment. Probably the terminology is not due to Artin. The Notre Dame lectures were in 1942 and published in 1944. In Emil Artin's 1947 lecture notes (notes taken by Albert A Blank, and seems to have been printed by Courant Institute; I'm not sure as I only have a photocopy) what normally is now called a Galois extension he calls a "normal extension" (he used normal differently from how it is used today).
This is also corroborated by a footnote in Hungerford's Algebra. In my edition the definition of a Galois extension (Definition 2.4 in Chapter V) has a footnote that reads (emphasis mine):
A Galois extension is frequently required to be finite dimensional or at least algebraic ... equivalent to the usual one. Our definition is essentially due to Artin, except that he calls such an extension "normal." Since this use of "normal" conflicts (in case char $Fneq 0$) with the definition of "normal" used by many other authors, we have chosen to follow Artin's basic approach, but to retain the (more or less) conventional terminology.
$endgroup$
Not an answer, but an extended comment. Probably the terminology is not due to Artin. The Notre Dame lectures were in 1942 and published in 1944. In Emil Artin's 1947 lecture notes (notes taken by Albert A Blank, and seems to have been printed by Courant Institute; I'm not sure as I only have a photocopy) what normally is now called a Galois extension he calls a "normal extension" (he used normal differently from how it is used today).
This is also corroborated by a footnote in Hungerford's Algebra. In my edition the definition of a Galois extension (Definition 2.4 in Chapter V) has a footnote that reads (emphasis mine):
A Galois extension is frequently required to be finite dimensional or at least algebraic ... equivalent to the usual one. Our definition is essentially due to Artin, except that he calls such an extension "normal." Since this use of "normal" conflicts (in case char $Fneq 0$) with the definition of "normal" used by many other authors, we have chosen to follow Artin's basic approach, but to retain the (more or less) conventional terminology.
answered Apr 10 at 15:26
community wiki
Willie Wong
add a comment |
add a comment |
Thanks for contributing an answer to MathOverflow!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathoverflow.net%2fquestions%2f327674%2fearliest-use-of-the-term-galois-extension%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
fVq5rh3BJeW,avAs,DJwgGuWL7ev,ecJ Lds4fTnX7vSDL,QuK4JmnxV,0 El
$begingroup$
The earliest occurrence in MathSciNet seems to be in the review of "Une généralisation de la notion de corps—corpoïde. Un corpoïde remarquable de la théorie des corps valués" by Marc Krasner, C. R. Acad. Sci. Paris 219, (1944) 345–347. The relevant sentence is "Commutative extension corpoids are discussed and Galois extensions defined."
$endgroup$
– Timothy Chow
Apr 11 at 2:49