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 $M_{ 15 }$
$\bigoplus_{i=1}^\infty F_2$ over
$\prod_{i=1}^\infty F_2$
Description:
$\bigoplus_{i=1}^\infty F_2$ as a module over $\prod_{i=1}^\infty F_2$
Reference(s):
(Citation needed)
Properties
Dimensions
Subsets
Known Properties
Name
amply supplemented
Bezout
co-Hopfian
distributive
divisible (naive)
faithful
finite uniform dimension
finitely cogenerated
finitely generated socle
finitely related
has a projective cover
Hopfian
nonsingular
projective
reflexive
singular
supplemented
top semisimple
torsion (naive)
$R_R$
Artinian
brick
coherent
cyclic
finite composition length
finitely generated
finitely presented
free
hollow
indecomposable
injective
linearly compact
local
Noetherian
simple
simple socle
strongly indecomposable
subdirectly irreducible
torsion (regular element)
uniform
uniserial
Bass module
clean
continuous
CS
essential socle
flat
Jacobson semisimple
nonzero socle
principally injective
proper Jacobson radical
quasi-continuous
quasi-injective
quasi-projective
semi-Artinian
semi-Noetherian
semi-reflexive
semisimple
serial
strongly semi-Noetherian
superfluous Jacobson radical
torsion-free
Legend
= has the property
= does not have the property
= information not in database
(Nothing was retrieved.)
(Nothing was retrieved.)