Results 1 to 2 of 2

Thread: Simple module: Let R be a ring with 1 and F a family of simple left R modules.

  1. #1
    New Member
    Join Date
    Jan 2015
    Posts
    34

    Simple module: Let R be a ring with 1 and F a family of simple left R modules.

    Please help me to prove the following result:


    Let [tex]R[/tex] be a ring with [tex]1[/tex] and [tex]\mathcal{F}[/tex] a family of simple left [tex]R[/tex] modules.


    Let [tex]M=\oplus_{S\in \mathcal{F}} S[/tex] and suppose that [tex]T[/tex] is a simple submodule of [tex]M[/tex].


    Show that [tex]T\cong S[/tex] for some [tex]S\in \mathcal{F}[/tex].


    Thanks
    Last edited by mmm4444bot; 02-06-2018 at 06:37 PM. Reason: replaced incorrect LaTex delimiters with [͏tex] and [͏/tex] tags

  2. #2
    Elite Member
    Join Date
    Jun 2007
    Posts
    17,454
    Quote Originally Posted by mona123 View Post
    Please help me to prove the following result:


    Let $R$ be a ring with $1$ and $\mathcal{F}$ a family of simple left $R$ modules.


    Let $M=\oplus_{S\in \mathcal{F}} S$ and suppose that $T$ is a simple submodule of $M$.


    Show that $T\cong S$ for some $S\in \mathcal{F}$.


    Thanks
    What are your thoughts?

    Please share your work with us ...even if you know it is wrong.

    If you are stuck at the beginning tell us and we'll start with the definitions.

    You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

    http://www.freemathhelp.com/forum/announcement.php?f=33
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

Tags for this Thread

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •