On the other hand, Bezout’s Lemma does not hold in that domain either; an example of a ring in which unique factorization fails but Bezout’s Lemma is true seems to be the ring of all algebraic integers. (I.e. all algebraic numbers solving a monic polynomial with integer coefficients)

]]>I find this _much_ easier to parse with the irrationality spelled out explicitly with an “i”. I literally missed the “-” five times, twice even after reading the more (to me) natural form on the Wikipedia page and thinking you’d made a mistake.

]]>see

http://en.wikipedia.org/wiki/Unique_factorisation_domain#Non-examples

for more.

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