Database of Ring Theory
Toggle navigation
Rings
Browse all rings
Search all rings
Browse commutative rings
Search commutative rings
Browse ring properties
Browse commutative ring properties
Search rings by keyword
Browse rings by dimension
Modules
Browse all modules
Search all modules
Browse module properties
Theorems
Citations
Contribute
Learn
FAQ
Login
Profile
Module $M_{ 21 }$
$\bigoplus_{i=1}^\infty \mathbb Z_{(2)}$ over
$\mathbb Z_{(2)}$
Description:
Direct sum of countably many copies of $\mathbb Z_{(2)}=$
$R_{69}$
Reference(s):
(Citation needed)
Properties
Dimensions
Subsets
Known Properties
Name
amply supplemented
clean
continuous
CS
divisible (naive)
essential socle
finitely generated socle
finitely related
injective
nonsingular
nonzero socle
principally injective
quasi-continuous
quasi-injective
reflexive
semi-Artinian
semi-Noetherian
simple socle
singular
supplemented
top semisimple
$R_R$
Artinian
Bass module
Bezout
brick
co-Hopfian
coherent
cyclic
distributive
finite composition length
finite uniform dimension
finitely cogenerated
finitely generated
finitely presented
hollow
Hopfian
indecomposable
Jacobson semisimple
linearly compact
local
Noetherian
semisimple
simple
strongly indecomposable
strongly semi-Noetherian
subdirectly irreducible
superfluous Jacobson radical
torsion (naive)
torsion (regular element)
uniform
uniserial
faithful
flat
free
has a projective cover
projective
proper Jacobson radical
quasi-projective
semi-reflexive
serial
torsion-free
Legend
= has the property
= does not have the property
= information not in database
(Nothing was retrieved.)
(Nothing was retrieved.)