PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (198)
Orphanage
Unclass'd
Unproven (490)
Corrections (7)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
Owner confidence rating: Low Entry average rating: No information on entry rating
zero module (Definition)

Let $ R$ be a ring.

The abelian group which contains only an identity element (zero) gains a trivial $ R$-module structure, which we call the zero module.

Every $ R$-module $ M$ has an zero element and thus a submodule consisting of that element. This is called the zero submodule of $ M$.



"zero module" is owned by antizeus.
(view preamble)

View style:

Other names:  zero submodule
Log in to rate this entry.
(view current ratings)

Cross-references: submodule, zero element, structure, identity element, contains, abelian group, ring
There are 3 references to this entry.

This is version 2 of zero module, born on 2001-11-24, modified 2003-09-20.
Object id is 1005, canonical name is ZeroModule.
Accessed 3785 times total.

Classification:
AMS MSC: 16D10 (Associative rings and algebras :: Modules, bimodules and ideals :: General module theory)
Pending Errata and Addenda
None.
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)