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Properties
Negator:
is
is not
Property:
---------
$R_R$
Artinian
Bass module
CS
Hopfian
Jacobson semisimple
Noetherian
amply supplemented
brick
clean
co-Hopfian
coherent
continuous
cyclic
distributive
divisible (naive)
essential socle
faithful
finite composition length
finite uniform dimension
finitely cogenerated
finitely generated
finitely generated socle
finitely presented
finitely related
flat
free
has a projective cover
hollow
indecomposable
injective
linearly compact
local
nonsingular
nonzero socle
principally injective
projective
proper Jacobson radical
quasi-continuous
quasi-injective
quasi-projective
reflexive
semi-Artinian
semi-Noetherian
semi-reflexive
semisimple
serial
simple
simple socle
singular
strongly indecomposable
strongly semi-Noetherian
subdirectly irreducible
superfluous Jacobson radical
supplemented
top semisimple
torsion (naive)
torsion (regular element)
torsion-free
uniform
uniserial
Negator:
is
is not
Property:
---------
$R_R$
Artinian
Bass module
CS
Hopfian
Jacobson semisimple
Noetherian
amply supplemented
brick
clean
co-Hopfian
coherent
continuous
cyclic
distributive
divisible (naive)
essential socle
faithful
finite composition length
finite uniform dimension
finitely cogenerated
finitely generated
finitely generated socle
finitely presented
finitely related
flat
free
has a projective cover
hollow
indecomposable
injective
linearly compact
local
nonsingular
nonzero socle
principally injective
projective
proper Jacobson radical
quasi-continuous
quasi-injective
quasi-projective
reflexive
semi-Artinian
semi-Noetherian
semi-reflexive
semisimple
serial
simple
simple socle
singular
strongly indecomposable
strongly semi-Noetherian
subdirectly irreducible
superfluous Jacobson radical
supplemented
top semisimple
torsion (naive)
torsion (regular element)
torsion-free
uniform
uniserial
Negator:
is
is not
Property:
---------
$R_R$
Artinian
Bass module
CS
Hopfian
Jacobson semisimple
Noetherian
amply supplemented
brick
clean
co-Hopfian
coherent
continuous
cyclic
distributive
divisible (naive)
essential socle
faithful
finite composition length
finite uniform dimension
finitely cogenerated
finitely generated
finitely generated socle
finitely presented
finitely related
flat
free
has a projective cover
hollow
indecomposable
injective
linearly compact
local
nonsingular
nonzero socle
principally injective
projective
proper Jacobson radical
quasi-continuous
quasi-injective
quasi-projective
reflexive
semi-Artinian
semi-Noetherian
semi-reflexive
semisimple
serial
simple
simple socle
singular
strongly indecomposable
strongly semi-Noetherian
subdirectly irreducible
superfluous Jacobson radical
supplemented
top semisimple
torsion (naive)
torsion (regular element)
torsion-free
uniform
uniserial