MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

How do we add elements in a quiver?

Please see here:

http://planetmath.org/encyclopedia/AdmissibleIdealsBoundQuiverAndItsAlgebra.html

I know how to multiply this (by concatenation) but how do we add them, i.e how do we interpet ab - c ? I don't understand why ab- c is not an element of $R^{2}$.

share|cite|improve this question

closed as off-topic by Stefan Kohl, Andrey Rekalo, j.c., Carlo Beenakker, David White Nov 6 '13 at 14:13

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question does not appear to be about research level mathematics within the scope defined in the help center." – Stefan Kohl, Andrey Rekalo, j.c., Carlo Beenakker, David White
If this question can be reworded to fit the rules in the help center, please edit the question.

3  
You should ask this on math.stackexchange.com – Mariano Suárez-Alvarez Oct 11 '11 at 15:48

Just formally, think of non-commuting variables in a polynomial ring.

share|cite|improve this answer
    
Thanks, can you please explain why ab - c is not an element of $R^{2}$? – New Oct 11 '11 at 16:09
2  
Is it simply because assuming it is true then ab is $R^{2}$ because it has length $2$ and since $R^{2}$ is an ideal then $R^{2}$ contains $ab-(ab-c)=c$ which has length $1$ so impossible? – New Oct 11 '11 at 16:11
    
Yes, that's right. – Julian Kuelshammer Oct 11 '11 at 16:18

Not the answer you're looking for? Browse other questions tagged or ask your own question.