Hello everybody, thanks for reading....
I've got this question that I don't seem to be able to solve on my own :-\
R is a ring. x is an nilpotent (?) element in it - meaning that there exists some n in N such that x^n = 0 (and x is not 0 of course).
There were some questions posed, and I got stuck on the last one:
prove that the element (x+u), where u is comutative with x (meaning xu=ux), is reversible (?) (meaning, that there exists an element r in R such that r*(x+u) = (x+u)*r = 1).
I try all the tricks up my sleeve and still am stuck.
a question before I've proved (1+x) is reversible, noticing that:
(1+x)(1-x+x^2-....+x^n-1) = 1 (since x^n is 0)... but this question seems much harder.
Thank you very much for reading/responding!
Thank you for the response.
However, I was not given the fact that u is invertible - only that it commutes with x (ux=xu)....
I'm sorry - I just reread the question and realized I am being given the fact that u is invertible :-)
Sorry again, thanks!