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Constructing a ring without unique factorisation

Published online by Cambridge University Press:  22 September 2016

Colin R. Fletcher  and
M. Lidster
Colin R. Fletcher
Affiliation:
Department of Pure Mathematics, University College of Wales, Penglais, Aberystwyth SY23 3BZ
M. Lidster
Affiliation:
Department of Pure Mathematics, University College of Wales, Penglais, Aberystwyth SY23 3BZ
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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]).

Type
Research Article
Information
The Mathematical Gazette , Volume 62 , Issue 420 , June 1978 , pp. 104 - 109
Copyright
Copyright © Mathematical Association 1978 

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References

1. Heath, T. L., The thirteen books of Euclid’s elements, Vol II. Cambridge University Press (1908).Google Scholar
2. Fletcher, C. R., Unique factorisation rings, Proc. Cambridge Phil. Soc. 65, 579–583 (1969).Google Scholar
3. Fletcher, C. R., Equivalent conditions for unique factorisation, Publ. Dept. Math. Lyon 8,13–22 (1971).Google Scholar