Deveno,
I was working on my iPad when I noticed you posted a reply to this thread
I accidentally unsubscribed from the thread ... moving too fast ...
Could you please re-post
Apologies to other members of MHF!
Peter
In Exercise 2 of Exercises 1-5 of John Dauns' book "Modules and Rings" we are given
and
where the matrix ring R acts on a right R-module whose elements are row vectors.
Find all submodules of M
Helped by Evgeny's post (See Math Help Boards) I commenced this problem as follows:
----------------------------------------------------------------------------------------
Typical elements of R are
where
Typical elements of M are (x,y) where
Now the elements of
Now to find submodules! (Approach is by trial and error - but surely there is a better way!)
Consider a set of the form - that is
Let and then test the action of R on M i.e. - that is test if
Now
But now a problem I hope someone can help with!
How do we (rigorously) evaluate and and hence check whether is of the form (x, 0) [certainly does not look like it but formally and rigorously ...?]
An example of my thinking here
If and then (roughly speaking!)
In the above I am assuming that in that that
and that
that
but I am not sure what I am doing here!
Can someone please clarify this situation?
Further, can someone please comment on my overall approach to the Exercise - I am not at all sure regarding how to check for submodules and certainly lack a systematic approach ...
Be grateful for some help ...
Peter
Deveno,
I was working on my iPad when I noticed you posted a reply to this thread
I accidentally unsubscribed from the thread ... moving too fast ...
Could you please re-post
Apologies to other members of MHF!
Peter