PRIME

Platonic

Realms

Interactive

Mathematics

Encyclopedia

 

algebraically closed

A field is algebraically closed if every polynomial with coefficients in the field has a root in the field.

Neither the field of rational numbers nor the field of real numbers is algebraically closed. For instance, the polynomial \(p(x)=x^2+2\) does not have a either a real or a rational root. However, it does have complex roots (\(\pm i \sqrt{2}\,\)), and indeed the field of complex numbers is algebraically closed.

Citation Info

  • [MLA] “algebraically closed.” Platonic Realms Interactive Mathematics Encyclopedia. Platonic Realms, 21 Feb 2013. Web. 21 Feb 2013. <http://platonicrealms.com/>
  • [APA] algebraically closed (21 Feb 2013). Retrieved 21 Feb 2013 from the Platonic Realms Interactive Mathematics Encyclopedia: http://platonicrealms.com/encyclopedia/algebraically-closed/

Advertisement

Get the ultimate math study-guide Math & Me: Embracing Successproduct thumbnail image Available in the Math Store
detail from Escher pic Belvedere

Are you a mathematical artist?

Platonic Realms is preparing an online gallery space to showcase and market the works of painters, sculptors, and other artists working in a tangible medium.

If your work celebrates mathematical themes we want to hear from you!

Please let us know about yourself using the contact page.