DaRT - Ring 116

Known Properties

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

Legend

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

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

Ring $R_{ 116 }$

$\mathbb Q[x,y,z]/(xz,yz)$

Description:

Reference(s):