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 $M_{ 9 }$
Indecomposable, not uniform module over
$F_2[x,y]/(x,y)^2$
Description:
The ring $F_2[x,y]/(x,y)^2$ as a regular module over itself
Reference(s):
(Citation needed)
Properties
Dimensions
Subsets
Known Properties
Name
singular
Bezout
brick
continuous
CS
distributive
divisible (naive)
injective
Jacobson semisimple
nonsingular
principally injective
quasi-continuous
quasi-injective
semisimple
serial
simple
simple socle
subdirectly irreducible
torsion (naive)
torsion (regular element)
uniform
uniserial
$R_R$
amply supplemented
Artinian
Bass module
clean
co-Hopfian
coherent
cyclic
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
linearly compact
local
Noetherian
nonzero socle
projective
proper Jacobson radical
quasi-projective
reflexive
semi-Artinian
semi-Noetherian
semi-reflexive
strongly indecomposable
strongly semi-Noetherian
superfluous Jacobson radical
supplemented
top semisimple
torsion-free
Legend
= has the property
= does not have the property
= information not in database
(Nothing was retrieved.)
(Nothing was retrieved.)