who coined the prime ideals?

Question

I know that Ernst Kummer first made used of "ideal complex numbers", and, hinging on that, Dedekind later introduced his "ideals" in Vorlesungen über Zahlentheorie. But, who coined the term "prime ideal"? Kummer? Dedekind? I would appreciate a specific reference to the work where they appear (a definition would be great). Thanks in advance.

Answer 1

It is Dedekind, in his $1871$'s paper Vorlesungen über Zahlentheorie von P.G. Lejeune Dirichlet who defines it : an ideal $\mathfrak{p}$ distinct from $\mathfrak{o}$ (ring of integers of a number field, as far as I remember the paper) and that has no other divisors that $\mathfrak{o}$ and $\mathfrak{p}$ is called a prime ideal. Bourbaki (in the historical notes to Algèbre or Algèbre commutative) mentions and confirms this.