Relation between finite fields $F_{p^2}$ and $F_p(omega)$.












0












$begingroup$


Let $F_p$ be a finite field having $p$ elements(for some prime $p$), not having primitive
$3$rd root of unit say $omega.$ Then can i say that field $F_p(omega)$ and $F_{p^2}$ are isomorphic.



I tried as follows: As both of fields $F_{p^{2}}$ and $F_p(omega)$ are of same dimension $2$ over the field $F_p$ and hence same number of elements. Now any two finite field with same number of elements are isomorphic.



Please suggest me. Thanks in advance.










share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    Yes, it is correct. Note that $omega$ is the root $x^2+x+1$, thus having order $2$.
    $endgroup$
    – Berci
    Dec 9 '18 at 10:43










  • $begingroup$
    Okh .... thanks .....
    $endgroup$
    – neelkanth
    Dec 9 '18 at 11:02
















0












$begingroup$


Let $F_p$ be a finite field having $p$ elements(for some prime $p$), not having primitive
$3$rd root of unit say $omega.$ Then can i say that field $F_p(omega)$ and $F_{p^2}$ are isomorphic.



I tried as follows: As both of fields $F_{p^{2}}$ and $F_p(omega)$ are of same dimension $2$ over the field $F_p$ and hence same number of elements. Now any two finite field with same number of elements are isomorphic.



Please suggest me. Thanks in advance.










share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    Yes, it is correct. Note that $omega$ is the root $x^2+x+1$, thus having order $2$.
    $endgroup$
    – Berci
    Dec 9 '18 at 10:43










  • $begingroup$
    Okh .... thanks .....
    $endgroup$
    – neelkanth
    Dec 9 '18 at 11:02














0












0








0


1



$begingroup$


Let $F_p$ be a finite field having $p$ elements(for some prime $p$), not having primitive
$3$rd root of unit say $omega.$ Then can i say that field $F_p(omega)$ and $F_{p^2}$ are isomorphic.



I tried as follows: As both of fields $F_{p^{2}}$ and $F_p(omega)$ are of same dimension $2$ over the field $F_p$ and hence same number of elements. Now any two finite field with same number of elements are isomorphic.



Please suggest me. Thanks in advance.










share|cite|improve this question











$endgroup$




Let $F_p$ be a finite field having $p$ elements(for some prime $p$), not having primitive
$3$rd root of unit say $omega.$ Then can i say that field $F_p(omega)$ and $F_{p^2}$ are isomorphic.



I tried as follows: As both of fields $F_{p^{2}}$ and $F_p(omega)$ are of same dimension $2$ over the field $F_p$ and hence same number of elements. Now any two finite field with same number of elements are isomorphic.



Please suggest me. Thanks in advance.







finite-fields






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 9 '18 at 9:34







neelkanth

















asked Dec 9 '18 at 8:56









neelkanthneelkanth

2,0742928




2,0742928








  • 1




    $begingroup$
    Yes, it is correct. Note that $omega$ is the root $x^2+x+1$, thus having order $2$.
    $endgroup$
    – Berci
    Dec 9 '18 at 10:43










  • $begingroup$
    Okh .... thanks .....
    $endgroup$
    – neelkanth
    Dec 9 '18 at 11:02














  • 1




    $begingroup$
    Yes, it is correct. Note that $omega$ is the root $x^2+x+1$, thus having order $2$.
    $endgroup$
    – Berci
    Dec 9 '18 at 10:43










  • $begingroup$
    Okh .... thanks .....
    $endgroup$
    – neelkanth
    Dec 9 '18 at 11:02








1




1




$begingroup$
Yes, it is correct. Note that $omega$ is the root $x^2+x+1$, thus having order $2$.
$endgroup$
– Berci
Dec 9 '18 at 10:43




$begingroup$
Yes, it is correct. Note that $omega$ is the root $x^2+x+1$, thus having order $2$.
$endgroup$
– Berci
Dec 9 '18 at 10:43












$begingroup$
Okh .... thanks .....
$endgroup$
– neelkanth
Dec 9 '18 at 11:02




$begingroup$
Okh .... thanks .....
$endgroup$
– neelkanth
Dec 9 '18 at 11:02










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
});


}
});














draft saved

draft discarded


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3032174%2frelation-between-finite-fields-f-p2-and-f-p-omega%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
















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.




draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3032174%2frelation-between-finite-fields-f-p2-and-f-p-omega%23new-answer', 'question_page');
}
);

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







Popular posts from this blog

Berounka

Sphinx de Gizeh

Different font size/position of beamer's navigation symbols template's content depending on regular/plain...