Ring $R_{ 80 }$

O'Meara's infinite matrix algebra

Description:

See the expanded details page.

Expanded details page.

Keywords Morita context infinite matrix ring matrix ring ring of functions

Reference(s):

K. C. O’Meara. A new setting for constructing von Neumann regular rings. (2017) @ Section 1

Symmetric properties

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

Asymmetric properties

left	Name	right
	ACC annihilator
	ACC principal
	Artinian
	Bezout
	Bezout domain
	cogenerator ring
	coherent
	cohopfian
	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
composition length	left: $\infty$	right: $\infty$

Name	Description
Jacobson radical	$\{0\}$