DaRT - Ring 128

Known Properties

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

Legend

= has the property
= does not have the property
= information not in database

Name	Description
Idempotents	$\{0,1\}$
Left singular ideal	$\{0\}$
Left socle	$\{0\}$
Nilpotents	$\{0\}$
Right singular ideal	$\{0\}$
Right socle	$\{0\}$
Zero divisors	$\{0\}$

Ring $R_{ 128 }$

Akizuki's counterexample

Description:

Reference(s):