Ring $R_{ 142 }$

Kaplansky's right-not-left hereditary ring

Description:

Let $S=$$R_{93}$. The required ring is $R=S\otimes_\mathbb Q S$

Keywords endomorphism ring subring tensor product

Reference(s):

I. Kaplansky. On the Dimension of Modules and Algebras, X: A Right Hereditary Ring which is not left Hereditary. (1958) @ Main theorem

Symmetric properties

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

Asymmetric properties

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

Legend

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

Name	Measure
global dimension	left: 2	right: 1
weak global dimension	0

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