Titlebook: Algebra; Serge Lang Textbook 2002Latest edition Springer Science+Business Media New York 2002 Algebra Textbook.Category theory.Textbook.al

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Vom ERM zur relationalen Datenbank,Presumably readers of this chapter will have had some basic acquaintance with linear algebra in elementary courses. We go beyond such courses by pointing out that a lot of results hold for free modules over a commutative ring. This is useful when one wants to deal with families of linear maps, and reduction modulo an ideal.

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RingsA .. is a set, together with two laws of composition called multiplication and addition respectively, and written as a product and as a sum respectively, satisfying the following conditions:

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Transcendental ExtensionsBoth for their own sake and for applications to the case of finite extensions of the rational numbers, one is led to deal with ground fields which are function fields, i.e. finitely generated over some field ., possibly by elements which are not algebraic. This chapter gives some basic properties of such fields.

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Matrices and Linear MapsPresumably readers of this chapter will have had some basic acquaintance with linear algebra in elementary courses. We go beyond such courses by pointing out that a lot of results hold for free modules over a commutative ring. This is useful when one wants to deal with families of linear maps, and reduction modulo an ideal.

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https://doi.org/10.1007/978-1-4613-0041-0Algebra Textbook; Category theory; Textbook; algebra; linear algebra; matrix theory

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978-1-4612-6551-1Springer Science+Business Media New York 2002