Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The sum of algebraic elements over a field is algebraic. Is there a way to write down an explicit equation of algebraic dependence for it, knowing the equations of algebraic dependence for the individual elements?

share|cite|improve this question
Have you tried writing down an equation for $\sqrt{2} + \sqrt[3]{3}$ (or even, $\sqrt{2} + \sqrt{3}$)? – Srivatsan Dec 4 '11 at 18:19
@Srivatsan: It doesn't seem difficult on a case by case basis. In your examples, I can isolate one of the radicals and keep raising to the appropriate powers. For example, with $x=\sqrt{2}+\sqrt{3}$, we have $(x-\sqrt{2})^2=3$. So $(x^2+1)^2=(2\sqrt{2}x)^2$ – Tomoki Visawa Dec 4 '11 at 18:26
Use tensor products. See Theorem 2.3 and Example 2.4 at – KCd Dec 4 '11 at 18:38
@KCd: Thank you. This is perfect. – Tomoki Visawa Dec 4 '11 at 18:42

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.