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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Correction to 'composite number'
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Too specific, only works for positive integers. by cgibbard
Correction id: 4713
Filed on: 2004-08-29 20:51:19
Status: Accepted on 2004-09-07 12:45:50
Type: Addendum
Correction text:
It would be nice if the definition at least worked for the integers, and it's not much harder to define the notion of a composite in any UFD. The positive integers don't quite form a ring, and so definitions that work for them might need a bit more work than usual to generalise.
Defining composite as the opposite of an irreducible would likely work well.
"If R is an integral domain, then n in R is called composite if n = a b for some non-units a and b."
Or if you want to be a bit more restrictive, but better capture the idea in all useful cases (this is equivalent in the case of a UFD),
"An element n in an integral domain is called composite if it can be expressed as the product of at least two primes."
Or perhaps
"A non-unit in an integral domain is called composite if it is not irreducible."
There are other ways of course, but these seem like the most natural ones to me. |
No comment from object owner mathcam.
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