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