Titlebook: Algebra I; Textbook for Student Alexey L. Gorodentsev Textbook 2016 Springer International Publishing AG 2016 Fields.Rings.Modules.Groups.L

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https://doi.org/10.1007/978-3-658-37268-2Throughout this chapter, we assume that ..

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Ideals, Quotient Rings, and Factorization,In this section we continue to use the notation of Chaps.?. and?4 and write . for an arbitrary commutative ring with unit and . for an arbitrary field.

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Determinants,Let . be a vector space of dimension . over a field .. We are going to define the . of a parallelepiped whose edges from some base vertex are . vectors ..,?..,?.,?.. as in Fig.?..

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Modules over a Principal Ideal Domain,In this chapter, . by default means an arbitrary commutative ring with unit and . means an arbitrary field. A .-. always means a unital module over ..

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Bilinear Forms,In this section we assume by default that ..

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Quadratic Forms and Quadrics,Throughout this chapter, we assume that ..

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