Back to the index. Or to the chambers
This article has 7 links. View as Cloud or List.
Ring Module Fancy Definition Of Module Maximal Element Submodule Automorphism Group Linear Code Krull Schmidt Theorem
| 1 | Ring |
| 1 | Module |
| 2 | Fancy Definition Of Module |
| 2 | Maximal Element |
| 3 | Automorphism Group Linear Code |
| 3 | Submodule |
| 7 | Krull Schmidt Theorem |
Loading ...
Planetmath Browser (2008—2009)
BSD licence | A django site
All articles taken from PlanetMath.org snapshot under CC-BY-SA licence.
→ The original article on PlanetMath.org
Other Formats: LaTeX
New! You can click on formulas to copy the LaTeX source to your clipboard. | Math Videos
Artinian
A module
is artinian
if it satisfies the following equivalent
conditions:
- the descending chain condition
holds for submodules
of
;
- every nonempty family of submodules of
has a minimal element.
A ring
is left artinian
if it is artinian as a left module
over itself
(i.e. if 
is an artinian module),
and right artinian
if it is artinian as a right module over itself
(i.e. if 
is an artinian module),
and simply artinian if both conditions hold.