Theorem

Krull's theorem on Jacobson polynomial rings

For a field $k$, the polynomial ring $k[\{X_i\mid i\in\mathbb N\}]$ is Jacobson if and only if $|k|$ is uncountable.

Reference(s)

  • W. Krull. Jacobsonsche Ringe, Hilbertscher Nullstellensatz, Dimensionstheorie. (1951) @ Satz 4, p. 363