Ring properties

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

2-primal Abelian ACC annihilator ACC principal algebraically closed field analytically normal analytically unramified Archimedean field Artinian atomic domain Baer Bezout Bezout domain catenary characteristic 0 field clean cogenerator ring Cohen-Macaulay coherent cohopfian commutative complete local compressible connected continuous 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 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 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 perfect perfect field $\pi$-regular polynomial identity 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 unit regular universally catenary universally Japanese valuation ring von Neumann regular V ring weakly clean Zorn