Ring $R_{ 198 }$

$\mathbb H[X]$

Description:

Ring of polynomials over the quaternions

Keywords polynomial ring

Reference(s):

(Citation needed)

Symmetric properties

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

Asymmetric properties

left	Name	right
	distributive
	duo
	finitely pseudo-Frobenius
	primitive
	quasi-duo
	Artinian
	cogenerator ring
	cohopfian
	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	$\{0\}$