Galois Group of Polynomial

Separable Polynomial
A polynomial over F is said to be separable if it has no multiple roots (i.e., all its roots are distinct).

Galois Group of Polynomial
Let f(x) be a separable polynomial over F. Let K be the splitting field over F of f(x). Then the Galois group of f(x) over F is defined to be \text{Gal}(K/F).

Author: mathtuition88

http://mathtuition88.com

Leave a Reply

Fill in your details below or click an icon to log in:

Gravatar
WordPress.com Logo

You are commenting using your WordPress.com account. ( Log Out /  Change )

Google photo

You are commenting using your Google account. ( Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. ( Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. ( Log Out /  Change )

Cancel

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.