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 (200)
Orphanage
Unclass'd
Unproven (490)
Corrections (6)
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
faithful module (Definition)

Let $ R$ be a ring, and let $ M$ be an $ R$-module. We say that $ M$ is a faithful $ R$-module if its annihilator $ {\rm ann}_R(M)$ is the zero ideal.

We say that $ M$ is a fully faithful $ R$-module if every nonzero $ R$-submodule of $ M$ is faithful.



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

View style:

Other names:  fully faithful module
Log in to rate this entry.
(view current ratings)

Cross-references: zero ideal, annihilator, faithful, ring
There is 1 reference to this entry.

This is version 3 of faithful module, born on 2001-11-24, modified 2003-09-20.
Object id is 999, canonical name is FaithfulModule.
Accessed 2685 times total.

Classification:
AMS MSC: 16D80 (Associative rings and algebras :: Modules, bimodules and ideals :: Other classes of modules and ideals)
Pending Errata and Addenda
None.
Discussion
Style: Expand: Order:
forum policy

No messages.

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