Commutative rings and related properties, II

[ ] J. D. O'Neill, An uncountable Noetherian ring with free additive group.
[ ] The integer-valued polynomials: elements of $\Bbb Q[x]$ which map $\Bbb Z$ to $\Bbb Z$.
[ ] The functions $\Bbb N \to \Bbb Z$ that are eventually rational polynomials (= Hilbert functions of graded modules.)
[ ] (if it's of interest) The ring of all functions $\Bbb Z \to \Bbb Z$.
(not a new ring) $R_{167}$ is isomorphic to Lazard's universal ring.
[ ] Novikov ring.
[ ] Rings of random variables with values in a commutative ring $R$. Note that if $|R| < \infty$, the sum of a uniform $R$-valued RV $U_1$ and an arbitrary RV $V_1$ independent from $U_1$ is also necessarily uniform. (A reference for these rings would be nice to have...)
"Jacobson (Hilbert)" was studied for noncommutative rings too (but only called by the first name), see 9.1.2 p342 McConnell, Robson; or Definition before Cor8.20 p147 Goodearl, Warfield. See also Cortzen, Small, Finite extensions of rings, the paragraph before Lemma p1059, and Th2 p1060.

rschwiebert / dart_data