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Constructing a ring without unique factorisation
Published online by Cambridge University Press: 22 September 2016
Extract
The study of unique factorisation is almost as old as mathematics itself. The so-called Fundamental Theorem of Arithmetic, which states that every integer greater than 1 can be factorised into a product of primes in only one way, was probably the first major theorem proved. It is interesting to note that Euclid (c. 300 B.C.) did not give the result in this form. He proved (IX 14) that “if a number be the least that is measured by prime numbers, it will not be measured by any other prime number except those originally measuring it” (see [1]).
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- Copyright © Mathematical Association 1978
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