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Basic Abstract Algebra by S. K. Jain, S. R. Nagpaul, P. B. Bhattacharya

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CHAPTER 11

Unique factorization domains and euclidean domains

1 Unique factorization domains

Throughout this chapter R is a commutative integral domain with unity. Such a ring is also called a domain.

If a and b are nonzero elements in R, we say that b divides a (or b is a divisor of a) and that a is divisible by b (or a is a multiple of b) if there exists in R an element c such that a = bc, and we write b|a or images (mod b). Clearly, an element images is a unit if and only if u is a divisor of 1.

Two elements a,b in R are called associates if there exists ...

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