2.5 Extension of homomorphisms. Uniqueness of algebraic closure.

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From the course by Higher School of Economics
Introduction to Galois Theory
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Higher School of Economics

Introduction to Galois Theory

79 ratings
From the lesson
Week 2
We introduce the notion of a stem field and a splitting field (of a polynomial). Using Zorn's lemma, we construct the algebraic closure of a field and deduce its unicity (up to an isomorphism) from the theorem on extension of homomorphisms.

Meet the Instructors

  • Ekaterina Amerik
    Ekaterina Amerik
    Professor
    Department of Mathematics