Kaup–Kupershmidt equation: Difference between revisions

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In [[mathematics]], an element ''r'' of a [[unique factorization domain]] ''R'' is called '''square-free''' if it is not [[integral domain|divisible]] by a non-trivial square. That is, every ''s'' such that <math>s^2\mid r</math> is a [[unit (algebra)|unit]] of ''R''.
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Square-free elements may be also characterized using their prime decomposition. The unique factorization property means that a non-zero non-unit ''r'' can be represented as a product of [[prime element]]s
:<math>r=p_1p_2\cdots p_n</math>
Then ''r'' is square-free if and only if the primes ''p<sub>i</sub>'' are pairwise [[associated element|non-associated]] (i.e. that it doesn't have two of the same prime as factors, which would make it divisible by a square number).
 
Common examples of square-free elements include [[square-free integer]]s and [[square-free polynomial]]s.
 
[[Category:Ring theory]]

Latest revision as of 16:37, 13 May 2014

Andrew Berryhill is what his spouse enjoys to call him and he completely digs that name. Credit authorising is exactly where my main earnings comes from. Ohio is where her house is. The preferred hobby for him and his children is to play lacross and he would never give it up.

My site: spirit messages (http://jplusfn.gaplus.kr/xe/qna/78647)

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