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Module $M_{ 11 }$
$(x)/(x^2)$ over
$\mathbb R[x]/(x^2)$
Description:
The ideal $(x)/(x^2)$ as a right $R$ module
Reference(s):
(Citation needed)
Properties
Dimensions
Subsets
Known Properties
Name
faithful
reflexive
torsion (naive)
$R_R$
divisible (naive)
flat
free
injective
nonsingular
principally injective
projective
torsion (regular element)
amply supplemented
Artinian
Bass module
Bezout
brick
clean
co-Hopfian
coherent
continuous
CS
cyclic
distributive
essential socle
finite composition length
finite uniform dimension
finitely cogenerated
finitely generated
finitely generated socle
finitely presented
finitely related
has a projective cover
hollow
Hopfian
indecomposable
Jacobson semisimple
linearly compact
local
Noetherian
nonzero socle
proper Jacobson radical
quasi-continuous
quasi-injective
quasi-projective
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-free
uniform
uniserial
Legend
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