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Module $M_{ 20 }$
$(x + (x,y)^2)$ over
$F_2[x,y]/(x,y)^2$
Description:
Ideal of $\mathbb F_2[x,y]/(x,y)^2$ generated by $x$
Reference(s):
(Citation needed)
Properties
Dimensions
Subsets
Known Properties
Name
divisible (naive)
injective
principally injective
torsion (naive)
$R_R$
faithful
flat
free
nonsingular
projective
reflexive
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
= has the property
= does not have the property
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