Titlebook: Galois Theory Through Exercises; Juliusz Brzeziński Textbook 2018 Springer International Publishing AG, part of Springer Nature 2018 Galoi

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Osmosis

978-3-319-72325-9Springer International Publishing AG, part of Springer Nature 2018

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Generosity

https://doi.org/10.1007/978-3-0348-7558-5This chapter contains the proofs to all theorems presented in the book. Only a few theorems, which are typically covered in an introductory course on groups, rings and fields are proved in the Appendix. A proof of the fundamental theorem of algebra is given in connection with the exercises in Chap. 13.

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John E. Souness,Mark A. GiembyczThis chapter contains hints and answers to all exercises presented in Chaps. .–. where an answer can be expected.

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Polynomials and Irreducibility,In this chapter, we present facts on zeros of polynomials and discuss some basic methods to decide whether a polynomial is irreducible or reducible, including Gauss’ lemma, the reduction of polynomials modulo prime numbers ((irreducibility over finite fields), and Eisenstein’s criterion.

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Proofs of the Theorems,This chapter contains the proofs to all theorems presented in the book. Only a few theorems, which are typically covered in an introductory course on groups, rings and fields are proved in the Appendix. A proof of the fundamental theorem of algebra is given in connection with the exercises in Chap. 13.