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Module $M_{ 1 }$
$\mathbb Z$ over
$\mathbb Z$: the ring of integers
Description:
Right regular module of the ring of integers.
Reference(s):
(Citation needed)
Properties
Dimensions
Subsets
Known Properties
Name
$R_R$
amply supplemented
Artinian
Bass module
Bezout
brick
clean
co-Hopfian
coherent
continuous
CS
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
Hopfian
indecomposable
injective
Jacobson semisimple
linearly compact
local
Noetherian
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
Legend
= has the property
= does not have the property
= information not in database
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