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Algebra: Abstract and Modern by U. M. Swamy, A. V. S. N. Murthy

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12

Factorization in Integral Domains

This chapter is concerned with the problem of factoring elements of an integral domain. The motivation for this lies in the ring ℤ of integers, where the Fundamental Theorem of Arithmetic states that every integer n > 1 can be written, in an essentially unique way, as a product of prime numbers; for example,

 

6,300 = 2 × 2 × 3 × 3 × 5 × 5 × 7

 

and 2, 3, 5 and 7 are prime numbers. In this chapter, we extend the factorization theory of the ring ℤ and, in particular, the above-mentioned Fundamental Theorem of Arithmetic, ...

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