Titlebook: Abstract Algebra; Suitable for Self-St Marco Hien Textbook 2024 The Editor(s) (if applicable) and The Author(s), under exclusive license to

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Einheiten des Strahlenschutzes,In this chapter, we examine which finite fields exist and how they are related to each other. The answer to the latter question will be provided by Galois theory.

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Kernenergie und Kernkraftwerke,We prove, as an application of Galois theory, that there are polynomial equations . over . of order . whose solutions cannot be solved by radicals. Considering the general equation, one can analogously see that there can be no solution formula for polynomial equations of degree 5 or higher.

ALTER

Defiance

Field Extensions and Algebraic Elements,Starting with a base field . and a polynomial equation with coefficients in ., one is naturally lead to involve a larger field . that contains the solutions. This leads to the concept of a field extension . | .. We investigate properties of those, which we mostly obtain from Linear Algebra.

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流动性

Unique Factorization Domains,An important tool in arithmetic inside the integers . is the unique prime factorization. We will take a closer look at this kind of property for rings—again not all rings will have this property.

GOAD

Obsequious

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