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Module $M_{ 7 }$
$\mathbb R[x_1,x_2,x_3,\ldots]$ over
$\mathbb R[x_1, x_2,x_3,\ldots]$
Description:
Right regular module of $\mathbb R[x_1,x_2,x_3,\ldots]$ over itself
Reference(s):
(Citation needed)
Properties
Dimensions
Subsets
Known Properties
Name
amply supplemented
Bezout
clean
Jacobson semisimple
semi-Noetherian
singular
strongly semi-Noetherian
supplemented
top semisimple
Artinian
brick
co-Hopfian
continuous
distributive
divisible (naive)
essential socle
finite composition length
finitely cogenerated
hollow
injective
linearly compact
local
Noetherian
nonzero socle
principally injective
quasi-injective
semi-Artinian
semisimple
serial
simple
simple socle
strongly indecomposable
subdirectly irreducible
torsion (naive)
torsion (regular element)
uniserial
$R_R$
Bass module
coherent
CS
cyclic
faithful
finite uniform dimension
finitely generated
finitely generated socle
finitely presented
finitely related
flat
free
has a projective cover
Hopfian
indecomposable
nonsingular
projective
proper Jacobson radical
quasi-continuous
quasi-projective
reflexive
semi-reflexive
superfluous Jacobson radical
torsion-free
uniform
Legend
= has the property
= does not have the property
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