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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Separability,In Chap.?. we saw that it is important to investigate whether an irreducible polynomial has multiple roots in an algebraic closure. This chapter clarifies this question.

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,Galois Theory (II)—The Fundamental Theorem,In this chapter, the fundamental theorem of Galois theory is stated and proven. Additionally, we prepare for application to the question of a solution formula for polynomial equations of higher degrees.

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Cyclotomic Fields,The cyclotomic fields, splitting fields of a polynomial of the form ., are interesting examples of fields that are well understood with the help of Galois theory. We will first consider these with an arbitrary base field, but then we will focus to the case . as the base field.

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Finite Fields,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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0302-9743 nd knowledge discovery, knowledge discovery and smart homes, smart learning environments, and visualization data analytics.978-3-642-39145-3978-3-642-39146-0Series ISSN 0302-9743 Series E-ISSN 1611-3349

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Ensemble Learning of Run-Time Prediction Models for Data-Intensive Scientific Workflowsting environments. Obtained results highlight the convenience of using ensemble models in comparison with single/standalone prediction models. Ensemble learning techniques permitted reductions of the prediction error up to 24.9% in comparison with single-model strategies.

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