Titlebook: Basic Algebra; Groups, Rings and Fi P. M. Cohn Textbook 2003 Springer-Verlag London Ltd., part of Springer Nature 2003 Algebra.Basic algebr

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Multilinear Algebra,nt example is given by free algebras, which are discussed in Section 6.2, as well as the related notions of tensor algebra and symmetric algebra on a .-module . A graded algebra has an important invariant, its Hilbert series, essentially a power series whose coefficients indicate the dimensions of t

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Field Theory,ction 7.1 field extensions are described, and the special case of splitting fields is introduced in Section 7.2, leading to the notion of algebraic closure (Section 7.3). In Section 7.4 we examine the problems arising in finite characteristic. One of the main tools in this study is Galois theory and

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Valuation Theory,mulation leads to the introduction of topological concepts like completion, which provides a powerful tool. It also emphasizes the parallel with the absolute value on the real and complex numbers. After the initial definitions (in Section 9.1) we shall prove the essential uniqueness of the absolute

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