Results 1 to 2 of 2

Math Help - Noetherian Ring

  1. #1
    Newbie
    Joined
    Nov 2007
    Posts
    2

    Noetherian Ring

    CONDITION 1:Let A is contained in B be aunitary commutative ring extension such that U(B) represents the set of units of B.For each b belong to B there exist d belong to U(B) and a belong to A such that b=da. NOTE:The conductor of A in B is the largest common ideal A:B={a belongs to A:aB is subset of A} of A and B.PROBLEM:Let A is contained in B be a domain extension which satisfies the condition 1 and M=A:B be a maximal ideal in A.Then B is Noetherian iff A is Noetherian.Moreover give an example
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    1)What does it mean "domain extension"? Does it simply mean A\subset B? And so B is an extension of A?
    2)Is A a commutative ring too? Or just a subset?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Ring theory, graded rings and noetherian rings
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: January 4th 2012, 11:46 AM
  2. every finite field is noetherian
    Posted in the Advanced Algebra Forum
    Replies: 10
    Last Post: March 21st 2011, 02:33 PM
  3. Noetherian Ring
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: September 7th 2010, 11:05 AM
  4. Noetherian ring, finitely generated module
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: May 5th 2009, 12:09 PM
  5. Non noetherian rings
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: May 13th 2006, 01:18 AM

Search Tags


/mathhelpforum @mathhelpforum