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...nt applications to other fields. These include the [[unique factorization|unique factorization theorem]], [[algebraic number fields]], [[elliptic curves]], and [[modular

{{r|Unique factorization}}

...e theory of vector spaces, in the same way that the [[unique factorization|unique factorization theorem]] is of fundamental importance in the study of integers. For insta

Euclid's lemma is used in the proof of the [[unique factorization theorem]], which states that a number cannot have more than one prime facto

{{r|Unique factorization}}

...sbaum published in 1959, it was shown that every regular local ring is a [[unique factorization domain]].

...he sum and the product now follows from the fact that every number has a [[unique factorization]] into primes. This also indicates the connection between the function <mat

The importance of prime numbers in arithmetic comes in large part from the [[unique factorization]] of numbers. The existence of a single unique factorization into prime numbers is formalized as the [[Fundamental Theorem of Arithmetic

The importance of prime numbers in arithmetic comes in large part from the [[unique factorization]] of numbers. ...imes 2 \times 7 \times 2 \times 3 \times 2 \times 5</math>. Because of the unique factorization of numbers into prime numbers, an analogy can be made between the role prim

I do think it is important to alter the very misleading statement about "unique factorization" in the currently approved version. [[User:Michael Hardy|Michael Hardy]] 22

** [[Unique factorization domain]] (UFD)