Solving Rings and Idempotent Problems - RK

  • Thread starter Thread starter cap.r
  • Start date Start date
  • Tags Tags
    Rings
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
1 reply · 2K views
cap.r
Messages
64
Reaction score
0
I have a tablet so I have made a PDF of all my work and the problem. the file is attached to this post. please let me know if i am on the right track or give me a hint. I am currently stuck in attempt 2 and don't like my solution in attempt 1.

attempt 1: at the very last step I am using multiplicative inverses and I haven't proved that they must exist. but since I have shown that a multiplicative identity is required, it shouldn't be hard to prove that inverses exist also but i don't know if it will be required..?

attempt 2: took a different approach at the problem, and while it's a bit more complicated in the end and is unfinished (this is where i am stuck), I think it's the better attempt.



thank you,
RK
 

Attachments

Physics news on Phys.org
a^3 = a implies that aaa = a.
Multiply by "a inverse" to obtain aa=1.
Multiply by "a inverse" again to obtain a=a^-1.
So each element is it's own inverse.