Ring properties

This is the comprehensive list of ring types used at present.

2-primal Abelian ACC annihilator ACC principal algebraically closed field almost Dedekind domain analytically normal analytically unramified Archimedean field Armendariz Artinian atomic domain Baer Bezout Bezout domain Boolean catenary characteristic 0 field clean cogenerator ring Cohen-Macaulay coherent cohopfian commutative complete local compressible connected continuous countable CS DCC annihilator Dedekind domain Dedekind finite distributive division ring domain dual duo essential socle Euclidean domain Euclidean field excellent exchange field FI-injective finite finitely cogenerated finitely generated socle finitely pseudo-Frobenius finite uniform dimension free ideal ring Frobenius fully prime fully semiprime GCD domain Goldie Goldman domain Gorenstein Grothendieck Henselian local hereditary $I_0$ IBN Ikeda-Nakayama J-0 J-1 J-2 Jacobson (Hilbert) Japanese (N-2) Kasch Krull domain lift/rad local local complete intersection max ring McCoy Mori domain N-1 Nagata nilpotent radical nil radical NI (nilpotents form an ideal) Noetherian nonsingular nonzero socle normal normal domain ordered field Ore domain Ore ring orthogonally finite PCI ring perfect perfect field periodic $\pi$-regular polynomial identity potent primary prime primitive principal ideal domain principal ideal ring principally injective Prufer domain pseudo-Frobenius Pythagorean field quadratically closed field quasi-continuous quasi-duo quasi-excellent quasi-Frobenius rad-nil reduced regular regular local reversible Rickart Schreier domain self-injective semicommutative (SI condition, zero-insertive) semi free ideal ring semihereditary semilocal semiperfect semiprimary semiprime semiprimitive semiregular semisimple serial simple simple Artinian simple-injective simple socle stable range 1 stably finite strongly connected strongly $\pi$-regular strongly regular symmetric T-nilpotent radical top regular top simple top simple Artinian uniform unique factorization domain uniserial ring unit regular universally catenary universally Japanese valuation domain von Neumann regular V ring weakly clean Zorn