Titlebook: A Concrete Introduction to Higher Algebra; Lindsay N. Childs Textbook 2009Latest edition Springer-Verlag New York 2009 algebra.field.finit

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Lindsay N. ChildsInformal and readable introduction to higher algebra.New sections on Luhn‘s formula, Cosets and equations, and detaching coefficients.Successful undergraduate text for more than 20 years

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Fazit: Klappe zu, Affe(kt) tot?,This chapter uses Bezout‘s identity and induction to prove the Fundamental Theorem of Arithmetic, that every natural number factors uniquely into a product of prime numbers. After exploring some initial consequences of the Fundamental Theorem, we introduce the study of prime numbers, a deep and fascinating area of number theory.

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https://doi.org/10.1007/978-3-476-05104-2The idea in this chapter is to use congruence to split up the set ? of integers into a finite collection of disjoint subsets, think of the subsets as objects, and then see if the arithmetic operations on ? can induce arithmetic operations on the new objects in a way that makes sense. To see how this might work, we first look at two examples.

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Kenneth T. Kishida,L. Paul SandsIn this chapter we introduce and apply to ?/.? some of the most basic concepts of “abstract” algebra: the concepts of group, ring, field, and ring homomorphism.

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Jonas Everaert,James J. Gross,Andero UusbergThe applications of Fermat‘s and Euler‘s Theorems in this chapter are to cryptography and to the study of large numbers.

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