Classifying homomorphisms on polynomial rings with real coefficients.
2
Show that every homomorphism $mathbb{R}$[X] $rightarrow$ $mathbb{R}$[X] can is equal to $φ_g$ for a unique g $in$ $mathbb{R}$[X], given by $φ_g(f)$ = $f(g(X))$
My guess for any homomorphism $h$, $g = h(X)$ but I'm not sure how to proceed from there.
abstract-algebra ring-homomorphism polynomial-rings
add a comment |
2
Show that every homomorphism $mathbb{R}$[X] $rightarrow$ $mathbb{R}$[X] can is equal to $φ_g$ for a unique g $in$ $mathbb{R}$[X], given by $φ_g(f)$ = $f(g(X))$
My guess for any homomorphism $h$, $g = h(X)$ but I'm not sure how to proceed from there.
abstract-algebra ring-homomorphism polynomial-rings
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 30 at 8:40
1
Your guess is right! Now you can directly calculate $h(f) = varphi_g(f)$ for any $f$ explicitly, using that $h$ is a homomorphism.
– Gnampfissimo
Nov 30 at 9:00
Every homomorphism of $mathbb R$-algebras, that is, fixing $mathbb R$.
– lhf
Nov 30 at 10:07
add a comment |
2
2
2
Show that every homomorphism $mathbb{R}$[X] $rightarrow$ $mathbb{R}$[X] can is equal to $φ_g$ for a unique g $in$ $mathbb{R}$[X], given by $φ_g(f)$ = $f(g(X))$
My guess for any homomorphism $h$, $g = h(X)$ but I'm not sure how to proceed from there.
abstract-algebra ring-homomorphism polynomial-rings
Show that every homomorphism $mathbb{R}$[X] $rightarrow$ $mathbb{R}$[X] can is equal to $φ_g$ for a unique g $in$ $mathbb{R}$[X], given by $φ_g(f)$ = $f(g(X))$
My guess for any homomorphism $h$, $g = h(X)$ but I'm not sure how to proceed from there.
abstract-algebra ring-homomorphism polynomial-rings
abstract-algebra ring-homomorphism polynomial-rings
asked Nov 30 at 8:40
user621286
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 30 at 8:40
1
Your guess is right! Now you can directly calculate $h(f) = varphi_g(f)$ for any $f$ explicitly, using that $h$ is a homomorphism.
– Gnampfissimo
Nov 30 at 9:00
Every homomorphism of $mathbb R$-algebras, that is, fixing $mathbb R$.
– lhf
Nov 30 at 10:07
add a comment |
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 30 at 8:40
1
Your guess is right! Now you can directly calculate $h(f) = varphi_g(f)$ for any $f$ explicitly, using that $h$ is a homomorphism.
– Gnampfissimo
Nov 30 at 9:00
Every homomorphism of $mathbb R$-algebras, that is, fixing $mathbb R$.
– lhf
Nov 30 at 10:07
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 30 at 8:40
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 30 at 8:40
1
1
Your guess is right! Now you can directly calculate $h(f) = varphi_g(f)$ for any $f$ explicitly, using that $h$ is a homomorphism.
– Gnampfissimo
Nov 30 at 9:00
Your guess is right! Now you can directly calculate $h(f) = varphi_g(f)$ for any $f$ explicitly, using that $h$ is a homomorphism.
– Gnampfissimo
Nov 30 at 9:00
Every homomorphism of $mathbb R$-algebras, that is, fixing $mathbb R$.
– lhf
Nov 30 at 10:07
Every homomorphism of $mathbb R$-algebras, that is, fixing $mathbb R$.
– lhf
Nov 30 at 10:07
add a comment |
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
});
}
});
draft saved
draft discarded
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%2f3019835%2fclassifying-homomorphisms-on-polynomial-rings-with-real-coefficients%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
draft saved
draft discarded
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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
To learn more, see our tips on writing great answers.
draft saved
draft discarded
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%2f3019835%2fclassifying-homomorphisms-on-polynomial-rings-with-real-coefficients%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
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 30 at 8:40
1
Your guess is right! Now you can directly calculate $h(f) = varphi_g(f)$ for any $f$ explicitly, using that $h$ is a homomorphism.
– Gnampfissimo
Nov 30 at 9:00
Every homomorphism of $mathbb R$-algebras, that is, fixing $mathbb R$.
– lhf
Nov 30 at 10:07