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What is Field Extensions and Splitting Fields about?

The document discusses field extensions, splitting fields, and perfect fields. It defines a splitting field as the smallest extension field of a given field that contains all the roots of a polynomial. It proves that for any non-constant polynomial over a field, there exists a field extension containing at least one root of the polynomial. It also gives examples of splitting fields, such as the splitting field of x3 - 2 over the rational numbers Q being Q(21/3, ω) where ω is the cube root of unity.

Author

Ayush Bhadauria

Language

EN