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Asymmetric properties
Negator:
is
is not
Property:
---------
ACC annihilator
ACC principal
Artinian
Bezout
Bezout domain
CS
DCC annihilator
FI-injective
Goldie
Ikeda-Nakayama
Kasch
McCoy
Noetherian
Ore domain
Ore ring
PCI ring
Rickart
T-nilpotent radical
UGP ring
V ring
co-Hopfian
cogenerator ring
coherent
continuous
distributive
dual
duo
essential socle
finite uniform dimension
finitely cogenerated
finitely generated socle
finitely pseudo-Frobenius
free ideal ring
hereditary
linearly compact
max ring
nonsingular
nonzero socle
perfect
primitive
principal ideal domain
principal ideal ring
principally injective
pseudo-Frobenius
quasi-continuous
quasi-duo
self-injective
semi-Artinian
semi-Noetherian
semihereditary
serial
simple socle
simple-injective
uniform
uniserial domain
uniserial ring
Side:
on the left
on the right
Negator:
is
is not
Property:
---------
ACC annihilator
ACC principal
Artinian
Bezout
Bezout domain
CS
DCC annihilator
FI-injective
Goldie
Ikeda-Nakayama
Kasch
McCoy
Noetherian
Ore domain
Ore ring
PCI ring
Rickart
T-nilpotent radical
UGP ring
V ring
co-Hopfian
cogenerator ring
coherent
continuous
distributive
dual
duo
essential socle
finite uniform dimension
finitely cogenerated
finitely generated socle
finitely pseudo-Frobenius
free ideal ring
hereditary
linearly compact
max ring
nonsingular
nonzero socle
perfect
primitive
principal ideal domain
principal ideal ring
principally injective
pseudo-Frobenius
quasi-continuous
quasi-duo
self-injective
semi-Artinian
semi-Noetherian
semihereditary
serial
simple socle
simple-injective
uniform
uniserial domain
uniserial ring
Side:
on the left
on the right
Negator:
is
is not
Property:
---------
ACC annihilator
ACC principal
Artinian
Bezout
Bezout domain
CS
DCC annihilator
FI-injective
Goldie
Ikeda-Nakayama
Kasch
McCoy
Noetherian
Ore domain
Ore ring
PCI ring
Rickart
T-nilpotent radical
UGP ring
V ring
co-Hopfian
cogenerator ring
coherent
continuous
distributive
dual
duo
essential socle
finite uniform dimension
finitely cogenerated
finitely generated socle
finitely pseudo-Frobenius
free ideal ring
hereditary
linearly compact
max ring
nonsingular
nonzero socle
perfect
primitive
principal ideal domain
principal ideal ring
principally injective
pseudo-Frobenius
quasi-continuous
quasi-duo
self-injective
semi-Artinian
semi-Noetherian
semihereditary
serial
simple socle
simple-injective
uniform
uniserial domain
uniserial ring
Side:
on the left
on the right
Symmetric properties
Negator:
is
is not
Property:
---------
$I_0$
$\pi$-regular
2-primal
Abelian
Armendariz
Baer
Boolean
Dedekind finite
Frobenius
IBN
IC ring
NI ring
Zorn
anti-automorphic
clean
commutative
compressible
countable
directly irreducible
division ring
domain
exchange
field
finite
fully prime
fully semiprime
involutive
lift/rad
local
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
subdirectly irreducible
symmetric
top regular
top simple
top simple Artinian
unit regular
von Neumann regular
weakly clean
Negator:
is
is not
Property:
---------
$I_0$
$\pi$-regular
2-primal
Abelian
Armendariz
Baer
Boolean
Dedekind finite
Frobenius
IBN
IC ring
NI ring
Zorn
anti-automorphic
clean
commutative
compressible
countable
directly irreducible
division ring
domain
exchange
field
finite
fully prime
fully semiprime
involutive
lift/rad
local
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
subdirectly irreducible
symmetric
top regular
top simple
top simple Artinian
unit regular
von Neumann regular
weakly clean
Negator:
is
is not
Property:
---------
$I_0$
$\pi$-regular
2-primal
Abelian
Armendariz
Baer
Boolean
Dedekind finite
Frobenius
IBN
IC ring
NI ring
Zorn
anti-automorphic
clean
commutative
compressible
countable
directly irreducible
division ring
domain
exchange
field
finite
fully prime
fully semiprime
involutive
lift/rad
local
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
subdirectly irreducible
symmetric
top regular
top simple
top simple Artinian
unit regular
von Neumann regular
weakly clean