Titlebook: Undergraduate Algebra; Serge Lang Textbook 19902nd edition Springer Science+Business Media New York 1990 Galois theory.Vector space.algebr

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Groups,.. is a set, together with a rule (called a .) which to each pair of elements ., . in . associates an element denoted by . in ., having the following properties.

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Rings,In this chapter, we axiomatize the notions of addition and multiplication.

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Polynomials,Let . be a field. Every reader of this book will have written expressions like . where ..,...,.. are real or complex numbers. We could also take these to be elements of .. But what does “.” mean? Or powers of “.” like ., ..,...,..?

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Field Theory,Let . be a subfield of a field .. We also say that . is an . of . and we denote the extension by .. Let . be a field. An element α in some extension of . is said to be . over . if there exists a non-zero polynomial .[.]such that .(α) = 0, i.e. if α satisfies a polynomial equation

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The Real and Complex Numbers,Let . be an integral ring. By an . of . one means a subset . of . satisfying the following conditions:

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Inelasticity

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