PlanetMath: module of finite rank

(more info)

Math for the people, by the people.

Main Menu

module of finite rank

(Definition)

Let be a module, and let be the injective hull of . Then we say that has finite rank if is a finite direct sum of indecomposable submodules.

This turns out to be equivalent to the property that has no infinite direct sums of nonzero submodules.

"module of finite rank" is owned by antizeus.

(view preamble)

Log in to rate this entry.
(view current ratings)

Cross-references: infinite, property, equivalent, submodules, indecomposable, direct sum, finite, injective hull, module
There are 4 references to this entry.

This is version 4 of module of finite rank, born on 2001-12-20, modified 2004-03-17.
Object id is 1106, canonical name is ModuleOfFiniteRank.
Accessed 2255 times total.

Classification:

16D80 (Associative rings and algebras :: Modules, bimodules and ideals :: Other classes of modules and ideals)

Pending Errata and Addenda

None.[ View all 3 ]

Discussion

forum policy

No messages.

Interact