can be uniquely decomposed as product of powers of prime numbers. It is also known as the fundamental theorem of arithmetic.

An element is a prime element if whenever divides a product , divides or . In a domain, being prime implies being irreducible. The converse is true in a unique factorization domain, but false in general.

Factor ring

The definition of ideals is such that "dividing" "out" gives another ring, the

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