Ring $R_{ 217 }$

$T_2(F_2)$

Description:

$R=T_2(F_2)$, the upper triangular matrices over the field of two elements $F_2$

Reference(s):

(Citation needed)

Symmetric properties

	Name
	Baer
	compressible
	subdirectly irreducible
	Abelian
	Armendariz
	Boolean
	commutative
	division ring
	domain
	field
	Frobenius
	fully prime
	fully semiprime
	local
	periodic
	primary
	prime
	quasi-Frobenius
	reduced
	reversible
	semi free ideal ring
	semicommutative
	semiprime
	semiprimitive
	semisimple
	simple
	simple Artinian
	strongly connected
	strongly regular
	symmetric
	top simple
	top simple Artinian
	unit regular
	von Neumann regular
	$\pi$-regular
	$I_0$
	2-primal
	anti-automorphic
	clean
	countable
	Dedekind finite
	directly irreducible
	exchange
	finite
	IBN
	IC ring
	involutive
	lift/rad
	NI ring
	nil radical
	nilpotent radical
	orthogonally finite
	polynomial identity
	potent
	semilocal
	semiperfect
	semiprimary
	semiregular
	stable range 1
	stably finite
	strongly $\pi$-regular
	top regular
	weakly clean
	Zorn

Asymmetric properties

left	Name	right
	ACC annihilator
	ACC principal
	Artinian
	Bezout
	Bezout domain
	co-Hopfian
	cogenerator ring
	coherent
	continuous
	CS
	DCC annihilator
	distributive
	dual
	duo
	essential socle
	FI-injective
	finite uniform dimension
	finitely cogenerated
	finitely generated socle
	finitely pseudo-Frobenius
	free ideal ring
	Goldie
	hereditary
	Ikeda-Nakayama
	Kasch
	linearly compact
	max ring
	McCoy
	Noetherian
	nonsingular
	nonzero socle
	Ore domain
	Ore ring
	PCI ring
	perfect
	primitive
	principal ideal domain
	principal ideal ring
	principally injective
	pseudo-Frobenius
	quasi-continuous
	quasi-duo
	Rickart
	self-injective
	semi-Artinian
	semi-Noetherian
	semihereditary
	serial
	simple socle
	simple-injective
	T-nilpotent radical
	UGP ring
	uniform
	uniserial domain
	uniserial ring
	V ring

Legend

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

Name	Measure
cardinality	8
global dimension	left: 1	right: 1
Krull dimension (classical)	0

Name	Description
Left singular ideal	$\{0\}$
Right singular ideal	$\{0\}$