# Elementary question about quiver [closed]

How do we add elements in a quiver?

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 $R^{2}$.

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

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

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

• Thanks, can you please explain why ab - c is not an element of $R^{2}$? – New Oct 11 '11 at 16:09
• 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