Results 1 to 2 of 2

Thread: Ideal in a conmmutative ring

  1. #1
    Newbie
    Joined
    Mar 2017
    From
    chile
    Posts
    22
    Thanks
    1

    Ideal in a conmmutative ring

    Hi! I have problems with this demostration


    Let I be an ideal in a commutative ring R. If J is an ideal in R and I\subseteq{J}, prove that:


    J/I = \{ r+I : r \in{J} \} is an ideal in R/I


    Demostration

    If J+I\in J/I, then J+I\in R/I because J\subset R, therefore J/I\subset R/I.

    Is the demonstration correct?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,454
    Thanks
    2728
    Awards
    1

    Re: Ideal in a conmmutative ring

    Quote Originally Posted by cristianoceli View Post
    Hi! I have problems with this demostration
    Let I be an ideal in a commutative ring R. If J is an ideal in R and I\subseteq{J}, prove that: J/I = \{ r+I : r \in{J} \} is an ideal in R/I
    Demostration
    If J+I\in J/I, then J+I\in R/I because J\subset R, therefore J/I\subset R/I.
    Is the demonstration correct?
    By Demostration I must assume that you mean PROOF.
    You ask: Is the demonstration correct?
    That depends upon what is required. What you have posted is correct under certain conditions.
    We have no way of knowing what your lecturer requires as a proof.
    For me, I expect a student to demonstrate that all conditions for $J/I$ to be an ideal in $R/I$ are meet.
    Have you done that?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: Apr 9th 2015, 12:19 AM
  2. ideal,nil,nilpotent ideal in prime ring
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 24th 2011, 08:57 AM
  3. Ideal of the ring
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Mar 27th 2011, 10:15 PM
  4. Ideal of ring
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Dec 16th 2009, 10:58 PM
  5. ring/ideal
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: Nov 19th 2009, 03:52 PM

/mathhelpforum @mathhelpforum