My Math Forum  

Go Back   My Math Forum > College Math Forum > Abstract Algebra

Abstract Algebra Abstract Algebra Math Forum

LinkBack Thread Tools Display Modes
June 5th, 2011, 03:30 AM   #1
Joined: Aug 2010

Posts: 32
Thanks: 0

Finitely generated injective extension

We know that every module has an injective extension; even we have a minimal injective extension known as "injective hall" or injective "envelope".
But this injective extension, even the minimal one, might not be finitely generated. For example consider the Noetherian Z-module Z; one can show that Q as Z-module is its injective hall, which is NOT finitely generated. It also follows that the Z-module Z has no finitely generated injective extension.

So my question is: For which kind of modules, under which conditions, we have a finitely generated injective extension for a module?
Snoopy is offline  

  My Math Forum > College Math Forum > Abstract Algebra

extension, finitely, generated, injective

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Prove S is not finitely generated. please help kennedy Linear Algebra 1 October 1st, 2009 03:59 PM
Noetherian, finitely generated R-module poincare4223 Abstract Algebra 0 April 29th, 2009 09:01 PM
Finitely Generated payman_pm Abstract Algebra 7 September 19th, 2007 04:21 AM
T-groups finitely generated sastra81 Abstract Algebra 0 January 3rd, 2007 06:54 AM
question about the groups finitely generated sastra81 Abstract Algebra 1 January 2nd, 2007 12:03 PM

Copyright © 2019 My Math Forum. All rights reserved.