Example
In the quadratic integer ring, it can be shown using norm arguments that the number 3 is irreducible. However, it is not a prime in this ring since, for example,
but does not divide either of the two factors.
Read more about this topic: Irreducible Element
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“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
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