Papers by Juliusz Brzezinski
Wiadomości Matematyczne, Jan 17, 2017
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Springer undergraduate mathematics series, 2018
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Springer undergraduate mathematics series, 2018
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Springer undergraduate mathematics series, 2018
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Springer undergraduate mathematics series, 2018
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Springer undergraduate mathematics series, 2018
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Springer undergraduate mathematics series, 2018
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Springer undergraduate mathematics series, 2018
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Springer undergraduate mathematics series, 2018
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Springer undergraduate mathematics series, 2018
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Springer undergraduate mathematics series, 2018
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Springer undergraduate mathematics series, 2018
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Springer undergraduate mathematics series, 2018
In this chapter, we study automorphism groups of fields and introduce Galois groups of finite fie... more In this chapter, we study automorphism groups of fields and introduce Galois groups of finite field extensions. The term “Galois group” is often reserved for automorphism groups of Galois field extensions, which we define and study in Chap. 9. The terminology used in this book is very common and has several advantages in textbooks (i.e. it is easier to formulate exercises). A central result of this chapter is Artin’s lemma, which is a key result in the modern presentation of Galois theory. In the exercises, we find Galois groups of many field extensions and we use also use this theorem for various problems on field extensions and their automorphism groups.
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Springer undergraduate mathematics series, 2018
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Springer undergraduate mathematics series, 2018
This chapter contains hints and answers to all exercises presented in Chaps. 1– 15 where an answe... more This chapter contains hints and answers to all exercises presented in Chaps. 1– 15 where an answer can be expected.
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Springer undergraduate mathematics series, 2018
In this chapter, we present facts on zeros of polynomials and discuss some basic methods to decid... more 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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arXiv (Cornell University), Aug 20, 2003
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Springer eBooks, 1985
Without Abstract
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Experimental Mathematics, 2005
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Canadian mathematical bulletin, Dec 1, 2006
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Papers by Juliusz Brzezinski