Just trying to get a grasp of what it means. Thanks!
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An algebraically closed field K is a field where any polynomial f(x) in K[x] has a zero in K.
For example, C is algebraically closed by the Fundamental Theorem of Algebra.
On the other hand, R is not algebraically closed, because x^2 + 1 has no zeros in R (since the zeros are -i and i).
Link:
http://en.wikipedia.org/wiki/Algebraical…
I hope this helps!
For example, C is algebraically closed by the Fundamental Theorem of Algebra.
On the other hand, R is not algebraically closed, because x^2 + 1 has no zeros in R (since the zeros are -i and i).
Link:
http://en.wikipedia.org/wiki/Algebraical…
I hope this helps!