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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
amply supplemented
clean
Jacobson semisimple
singular
supplemented
top semisimple
Artinian
brick
co-Hopfian
continuous
divisible (naive)
essential socle
finite composition length
finitely cogenerated
hollow
injective
linearly compact
local
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
Bezout
coherent
CS
cyclic
distributive
faithful
finite uniform dimension
finitely generated
finitely generated socle
finitely presented
finitely related
flat
free
has a projective cover
Hopfian
indecomposable
Noetherian
nonsingular
projective
proper Jacobson radical
quasi-continuous
quasi-projective
reflexive
semi-Noetherian
semi-reflexive
strongly semi-Noetherian
superfluous Jacobson radical
torsion-free
uniform
Legend
= has the property
= does not have the property
= information not in database
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