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Properties
Negator:
is
is not
Property:
---------
$I_0$
$\pi$-regular
2-primal
Abelian
ACC annihilator
ACC principal
algebraically closed field
almost Dedekind domain
analytically normal
analytically unramified
Archimedean field
Armendariz
Artinian
atomic domain
Baer
Bezout
Bezout domain
Boolean
catenary
characteristic 0 field
clean
cogenerator ring
Cohen-Macaulay
coherent
cohopfian
commutative
complete local
compressible
connected
continuous
countable
CS
DCC annihilator
Dedekind domain
Dedekind finite
distributive
division ring
domain
dual
duo
essential socle
Euclidean domain
Euclidean field
excellent
exchange
field
FI-injective
finite
finitely cogenerated
finitely generated socle
finitely pseudo-Frobenius
finite uniform dimension
free ideal ring
Frobenius
fully prime
fully semiprime
GCD domain
Goldie
Goldman domain
Gorenstein
Grothendieck
Henselian local
hereditary
IBN
Ikeda-Nakayama
J-0
J-1
J-2
Jacobson (Hilbert)
Japanese (N-2)
Kasch
Krull domain
lift/rad
local
local complete intersection
max ring
McCoy
Mori domain
N-1
Nagata
nilpotent radical
nil radical
NI (nilpotents form an ideal)
Noetherian
nonsingular
nonzero socle
normal
normal domain
ordered field
Ore domain
Ore ring
orthogonally finite
PCI ring
perfect
perfect field
periodic
polynomial identity
potent
primary
prime
primitive
principal ideal domain
principal ideal ring
principally injective
Prufer domain
pseudo-Frobenius
Pythagorean field
quadratically closed field
quasi-continuous
quasi-duo
quasi-excellent
quasi-Frobenius
rad-nil
reduced
regular
regular local
reversible
Rickart
Schreier domain
self-injective
semicommutative (SI condition, zero-insertive)
semi free ideal ring
semihereditary
semilocal
semiperfect
semiprimary
semiprime
semiprimitive
semiregular
semisimple
serial
simple
simple Artinian
simple-injective
simple socle
stable range 1
stably finite
strongly $\pi$-regular
strongly connected
strongly regular
symmetric
T-nilpotent radical
top regular
top simple
top simple Artinian
uniform
unique factorization domain
uniserial ring
unit regular
universally catenary
universally Japanese
valuation domain
von Neumann regular
V ring
weakly clean
Zorn
Negator:
is
is not
Property:
---------
$I_0$
$\pi$-regular
2-primal
Abelian
ACC annihilator
ACC principal
algebraically closed field
almost Dedekind domain
analytically normal
analytically unramified
Archimedean field
Armendariz
Artinian
atomic domain
Baer
Bezout
Bezout domain
Boolean
catenary
characteristic 0 field
clean
cogenerator ring
Cohen-Macaulay
coherent
cohopfian
commutative
complete local
compressible
connected
continuous
countable
CS
DCC annihilator
Dedekind domain
Dedekind finite
distributive
division ring
domain
dual
duo
essential socle
Euclidean domain
Euclidean field
excellent
exchange
field
FI-injective
finite
finitely cogenerated
finitely generated socle
finitely pseudo-Frobenius
finite uniform dimension
free ideal ring
Frobenius
fully prime
fully semiprime
GCD domain
Goldie
Goldman domain
Gorenstein
Grothendieck
Henselian local
hereditary
IBN
Ikeda-Nakayama
J-0
J-1
J-2
Jacobson (Hilbert)
Japanese (N-2)
Kasch
Krull domain
lift/rad
local
local complete intersection
max ring
McCoy
Mori domain
N-1
Nagata
nilpotent radical
nil radical
NI (nilpotents form an ideal)
Noetherian
nonsingular
nonzero socle
normal
normal domain
ordered field
Ore domain
Ore ring
orthogonally finite
PCI ring
perfect
perfect field
periodic
polynomial identity
potent
primary
prime
primitive
principal ideal domain
principal ideal ring
principally injective
Prufer domain
pseudo-Frobenius
Pythagorean field
quadratically closed field
quasi-continuous
quasi-duo
quasi-excellent
quasi-Frobenius
rad-nil
reduced
regular
regular local
reversible
Rickart
Schreier domain
self-injective
semicommutative (SI condition, zero-insertive)
semi free ideal ring
semihereditary
semilocal
semiperfect
semiprimary
semiprime
semiprimitive
semiregular
semisimple
serial
simple
simple Artinian
simple-injective
simple socle
stable range 1
stably finite
strongly $\pi$-regular
strongly connected
strongly regular
symmetric
T-nilpotent radical
top regular
top simple
top simple Artinian
uniform
unique factorization domain
uniserial ring
unit regular
universally catenary
universally Japanese
valuation domain
von Neumann regular
V ring
weakly clean
Zorn
Negator:
is
is not
Property:
---------
$I_0$
$\pi$-regular
2-primal
Abelian
ACC annihilator
ACC principal
algebraically closed field
almost Dedekind domain
analytically normal
analytically unramified
Archimedean field
Armendariz
Artinian
atomic domain
Baer
Bezout
Bezout domain
Boolean
catenary
characteristic 0 field
clean
cogenerator ring
Cohen-Macaulay
coherent
cohopfian
commutative
complete local
compressible
connected
continuous
countable
CS
DCC annihilator
Dedekind domain
Dedekind finite
distributive
division ring
domain
dual
duo
essential socle
Euclidean domain
Euclidean field
excellent
exchange
field
FI-injective
finite
finitely cogenerated
finitely generated socle
finitely pseudo-Frobenius
finite uniform dimension
free ideal ring
Frobenius
fully prime
fully semiprime
GCD domain
Goldie
Goldman domain
Gorenstein
Grothendieck
Henselian local
hereditary
IBN
Ikeda-Nakayama
J-0
J-1
J-2
Jacobson (Hilbert)
Japanese (N-2)
Kasch
Krull domain
lift/rad
local
local complete intersection
max ring
McCoy
Mori domain
N-1
Nagata
nilpotent radical
nil radical
NI (nilpotents form an ideal)
Noetherian
nonsingular
nonzero socle
normal
normal domain
ordered field
Ore domain
Ore ring
orthogonally finite
PCI ring
perfect
perfect field
periodic
polynomial identity
potent
primary
prime
primitive
principal ideal domain
principal ideal ring
principally injective
Prufer domain
pseudo-Frobenius
Pythagorean field
quadratically closed field
quasi-continuous
quasi-duo
quasi-excellent
quasi-Frobenius
rad-nil
reduced
regular
regular local
reversible
Rickart
Schreier domain
self-injective
semicommutative (SI condition, zero-insertive)
semi free ideal ring
semihereditary
semilocal
semiperfect
semiprimary
semiprime
semiprimitive
semiregular
semisimple
serial
simple
simple Artinian
simple-injective
simple socle
stable range 1
stably finite
strongly $\pi$-regular
strongly connected
strongly regular
symmetric
T-nilpotent radical
top regular
top simple
top simple Artinian
uniform
unique factorization domain
uniserial ring
unit regular
universally catenary
universally Japanese
valuation domain
von Neumann regular
V ring
weakly clean
Zorn