Abstract
In this first chapter concerning polynomial equations, we show that given a polynomial over a field, there always exists some extension of the field where the polynomial has a root, and we prove the existence of an algebraic closure. We make a preliminary study of such extensions, including the automorphisms, and we give algebraic extensions of finite fields as examples.
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© 2002 Springer Science+Business Media New York
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Lang, S. (2002). Algebraic Extensions. In: Algebra. Graduate Texts in Mathematics, vol 211. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0041-0_5
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DOI: https://doi.org/10.1007/978-1-4613-0041-0_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6551-1
Online ISBN: 978-1-4613-0041-0
eBook Packages: Springer Book Archive