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Asymmetric properties
Negator:
is
is not
Property:
---------
ACC annihilator
ACC principal
Artinian
Bezout
Bezout domain
cogenerator ring
coherent
cohopfian
continuous
CS
DCC annihilator
distributive
dual
duo
essential socle
FI-injective
finitely cogenerated
finitely generated socle
finitely pseudo-Frobenius
finite uniform dimension
free ideal ring
Goldie
hereditary
Ikeda-Nakayama
Kasch
Noetherian
nonsingular
nonzero socle
Ore domain
Ore ring
perfect
primitive
principal ideal domain
principal ideal ring
principally injective
pseudo-Frobenius
quasi-continuous
quasi-duo
Rickart
self-injective
semihereditary
serial
simple-injective
simple socle
T-nilpotent radical
uniform
valuation ring
V ring
Side:
on the left
on the right
Negator:
is
is not
Property:
---------
ACC annihilator
ACC principal
Artinian
Bezout
Bezout domain
cogenerator ring
coherent
cohopfian
continuous
CS
DCC annihilator
distributive
dual
duo
essential socle
FI-injective
finitely cogenerated
finitely generated socle
finitely pseudo-Frobenius
finite uniform dimension
free ideal ring
Goldie
hereditary
Ikeda-Nakayama
Kasch
Noetherian
nonsingular
nonzero socle
Ore domain
Ore ring
perfect
primitive
principal ideal domain
principal ideal ring
principally injective
pseudo-Frobenius
quasi-continuous
quasi-duo
Rickart
self-injective
semihereditary
serial
simple-injective
simple socle
T-nilpotent radical
uniform
valuation ring
V ring
Side:
on the left
on the right
Negator:
is
is not
Property:
---------
ACC annihilator
ACC principal
Artinian
Bezout
Bezout domain
cogenerator ring
coherent
cohopfian
continuous
CS
DCC annihilator
distributive
dual
duo
essential socle
FI-injective
finitely cogenerated
finitely generated socle
finitely pseudo-Frobenius
finite uniform dimension
free ideal ring
Goldie
hereditary
Ikeda-Nakayama
Kasch
Noetherian
nonsingular
nonzero socle
Ore domain
Ore ring
perfect
primitive
principal ideal domain
principal ideal ring
principally injective
pseudo-Frobenius
quasi-continuous
quasi-duo
Rickart
self-injective
semihereditary
serial
simple-injective
simple socle
T-nilpotent radical
uniform
valuation ring
V ring
Side:
on the left
on the right
Symmetric properties
Negator:
is
is not
Property:
---------
2-primal
Abelian
Baer
clean
commutative
compressible
connected
Dedekind finite
division ring
domain
exchange
field
finite
Frobenius
fully prime
fully semiprime
$I_0$
IBN
lift/rad
local
nilpotent radical
nil radical
NI (nilpotents form an ideal)
orthogonally finite
$\pi$-regular
polynomial identity
primary
prime
quasi-Frobenius
reduced
reversible
semicommutative (SI condition, zero-insertive)
semi free ideal ring
semilocal
semiperfect
semiprimary
semiprime
semiprimitive
semiregular
semisimple
simple
simple Artinian
stable range 1
stably finite
strongly connected
strongly $\pi$-regular
strongly regular
symmetric
top regular
top simple
top simple Artinian
unit regular
von Neumann regular
weakly clean
Zorn
Negator:
is
is not
Property:
---------
2-primal
Abelian
Baer
clean
commutative
compressible
connected
Dedekind finite
division ring
domain
exchange
field
finite
Frobenius
fully prime
fully semiprime
$I_0$
IBN
lift/rad
local
nilpotent radical
nil radical
NI (nilpotents form an ideal)
orthogonally finite
$\pi$-regular
polynomial identity
primary
prime
quasi-Frobenius
reduced
reversible
semicommutative (SI condition, zero-insertive)
semi free ideal ring
semilocal
semiperfect
semiprimary
semiprime
semiprimitive
semiregular
semisimple
simple
simple Artinian
stable range 1
stably finite
strongly connected
strongly $\pi$-regular
strongly regular
symmetric
top regular
top simple
top simple Artinian
unit regular
von Neumann regular
weakly clean
Zorn
Negator:
is
is not
Property:
---------
2-primal
Abelian
Baer
clean
commutative
compressible
connected
Dedekind finite
division ring
domain
exchange
field
finite
Frobenius
fully prime
fully semiprime
$I_0$
IBN
lift/rad
local
nilpotent radical
nil radical
NI (nilpotents form an ideal)
orthogonally finite
$\pi$-regular
polynomial identity
primary
prime
quasi-Frobenius
reduced
reversible
semicommutative (SI condition, zero-insertive)
semi free ideal ring
semilocal
semiperfect
semiprimary
semiprime
semiprimitive
semiregular
semisimple
simple
simple Artinian
stable range 1
stably finite
strongly connected
strongly $\pi$-regular
strongly regular
symmetric
top regular
top simple
top simple Artinian
unit regular
von Neumann regular
weakly clean
Zorn