> I think that distinguishing between is_prime and is_prime_element
> is very very confusing.    And I agree with John Cremona that
> "prime" is not a very useful notation in algebraic number
> theory / commutative algebra for *elements* -- it's a great
> notion for ideals.

While it may not be terribly useful in those areas, I wouldn't rule it
out for all of ring theory.  As someone who doesn't do number theory,
the number theoretic definition of prime feels really weird.

--Mike

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