Ring $R_{ 199 }$

$M_2(\mathbb H[X])$

Description:

The ring of $2\times 2$ matrices over the ring $\mathbb H[X]$.

Keywords matrix ring polynomial ring

Reference(s):

D. Khurana and T. Lam. Rings with internal cancellation. (2005) @ Proposition 5.10 p 215

Symmetric properties

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

Asymmetric properties

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

Legend

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

Name	Measure
global dimension	left: 1	right: 1

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