Isomorphism of quotient by prime ideal and quotient of localization The Next CEO of Stack OverflowCorrespondence between valuations and prime idealsFind primitive element such that conductor is relatively prime to an ideal (exercise from Neukirch)Atiyah - Macdonald Exericse 9.7 via LocalizationIdeals in a Dedekind domain localized at a prime idealfractional ideals in the localization of a DedekindA proof in Janusz Algebraic Number Fieldideal and ideal classes in the ring of integers.Non maximal prime ideals and localizationIntegral and prime ideal in Dedekind domainThere exist an integral ideal prime to a given nonzero integral ideal
Science fiction novels about a solar system spanning civilisation where people change their bodies at will
Return of the Riley Riddles in Reverse
Describing a person. What needs to be mentioned?
Unreliable Magic - Is it worth it?
How do scammers retract money, while you can’t?
Science fiction (dystopian) short story set after WWIII
How to be diplomatic in refusing to write code that breaches the privacy of our users
How do spells that require an ability check vs. the caster's spell save DC work?
What is the point of a new vote on May's deal when the indicative votes suggest she will not win?
What's the point of interval inversion?
Why does GHC infer a monomorphic type here, even with MonomorphismRestriction disabled?
Anatomically Correct Mesopelagic Aves
Trouble understanding the speech of overseas colleagues
What is meant by a M next to a roman numeral?
Why were Madagascar and New Zealand discovered so late?
What can we do to stop prior company from asking us questions?
Return the Closest Prime Number
Whats the best way to handle refactoring a big file?
Fastest way to shutdown Ubuntu Mate 18.10
How to make a variable always equal to the result of some calculations?
Can a single photon have an energy density?
Where to find order of arguments for default functions
How to make a software documentation "officially" citable?
How do I solve this limit?
Isomorphism of quotient by prime ideal and quotient of localization
The Next CEO of Stack OverflowCorrespondence between valuations and prime idealsFind primitive element such that conductor is relatively prime to an ideal (exercise from Neukirch)Atiyah - Macdonald Exericse 9.7 via LocalizationIdeals in a Dedekind domain localized at a prime idealfractional ideals in the localization of a DedekindA proof in Janusz Algebraic Number Fieldideal and ideal classes in the ring of integers.Non maximal prime ideals and localizationIntegral and prime ideal in Dedekind domainThere exist an integral ideal prime to a given nonzero integral ideal
$begingroup$
Let $R$ be an integral domain.
$mathfrakp$ be a prime ideal of $R$.
Let $R_mathfrakp$ be localization of $R$ at $mathfrakp$.
Then an exercise in Algebraic Number Fields-Janusz asks
There is isomorphism between the fields $R/mathfrakp$ and $R_mathfrakp/mathfrakpR_mathfrakp$.
I think, $mathfrakp$ should be maximal, otherwise $R/mathfrakp$ is an integral domain and it always embeds in $R_mathfrakp/mathfrakpR_mathfrakp$; but isomorphism is not always possible. Am I right?
So question is simply that $mathfrakp$ should be maximal ideal to prove above assertion, is this right?
algebraic-number-theory
asked yesterday
BeginnerBeginner
4,00611226
$endgroup$
add a comment |
$begingroup$
Let $R$ be an integral domain.
$mathfrakp$ be a prime ideal of $R$.
Let $R_mathfrakp$ be localization of $R$ at $mathfrakp$.
Then an exercise in Algebraic Number Fields-Janusz asks
There is isomorphism between the fields $R/mathfrakp$ and $R_mathfrakp/mathfrakpR_mathfrakp$.
I think, $mathfrakp$ should be maximal, otherwise $R/mathfrakp$ is an integral domain and it always embeds in $R_mathfrakp/mathfrakpR_mathfrakp$; but isomorphism is not always possible. Am I right?
So question is simply that $mathfrakp$ should be maximal ideal to prove above assertion, is this right?
algebraic-number-theory
asked yesterday
BeginnerBeginner
4,00611226
$endgroup$
$begingroup$
Here you can find a generalization and a proof of the statement.
$endgroup$
– Fabio Lucchini
yesterday
add a comment |
$begingroup$
Let $R$ be an integral domain.
$mathfrakp$ be a prime ideal of $R$.
Let $R_mathfrakp$ be localization of $R$ at $mathfrakp$.
Then an exercise in Algebraic Number Fields-Janusz asks
There is isomorphism between the fields $R/mathfrakp$ and $R_mathfrakp/mathfrakpR_mathfrakp$.
I think, $mathfrakp$ should be maximal, otherwise $R/mathfrakp$ is an integral domain and it always embeds in $R_mathfrakp/mathfrakpR_mathfrakp$; but isomorphism is not always possible. Am I right?
So question is simply that $mathfrakp$ should be maximal ideal to prove above assertion, is this right?
algebraic-number-theory
asked yesterday
BeginnerBeginner
4,00611226
$endgroup$
Let $R$ be an integral domain.
$mathfrakp$ be a prime ideal of $R$.
Let $R_mathfrakp$ be localization of $R$ at $mathfrakp$.
Then an exercise in Algebraic Number Fields-Janusz asks
There is isomorphism between the fields $R/mathfrakp$ and $R_mathfrakp/mathfrakpR_mathfrakp$.
I think, $mathfrakp$ should be maximal, otherwise $R/mathfrakp$ is an integral domain and it always embeds in $R_mathfrakp/mathfrakpR_mathfrakp$; but isomorphism is not always possible. Am I right?
So question is simply that $mathfrakp$ should be maximal ideal to prove above assertion, is this right?
algebraic-number-theory
algebraic-number-theory
asked yesterday
BeginnerBeginner
4,00611226
asked yesterday
BeginnerBeginner
4,00611226
asked yesterday
BeginnerBeginner
4,00611226
asked yesterday
BeginnerBeginner
4,00611226
asked yesterday
BeginnerBeginner
4,00611226
4,00611226
$begingroup$
Here you can find a generalization and a proof of the statement.
$endgroup$
– Fabio Lucchini
yesterday
add a comment |
$begingroup$
Here you can find a generalization and a proof of the statement.
$endgroup$
– Fabio Lucchini
yesterday
$begingroup$
Here you can find a generalization and a proof of the statement.
$endgroup$
– Fabio Lucchini
yesterday
$begingroup$
Here you can find a generalization and a proof of the statement.
$endgroup$
– Fabio Lucchini
yesterday
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
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%2fmath.stackexchange.com%2fquestions%2f3164326%2fisomorphism-of-quotient-by-prime-ideal-and-quotient-of-localization%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- 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%2fmath.stackexchange.com%2fquestions%2f3164326%2fisomorphism-of-quotient-by-prime-ideal-and-quotient-of-localization%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
$begingroup$
Here you can find a generalization and a proof of the statement.
$endgroup$
– Fabio Lucchini
yesterday