Ring $R_{ 198 }$

$\mathbb H[X]$

Description:

Ring of polynomials over the quaternions

Keywords polynomial ring

Reference(s):

(Citation needed)

Symmetric properties

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

Asymmetric properties

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

Legend

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

Name	Measure
global dimension	left: 1	right: 1

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