How do we add elements in a quiver?
Please see here:
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 $R^{2}$.
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3$\begingroup$ You should ask this on math.stackexchange.com $\endgroup$– Mariano Suárez-ÁlvarezOct 11, 2011 at 15:48
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1 Answer
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Just formally, think of non-commuting variables in a polynomial ring.
answered Oct 11, 2011 at 16:01
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$\begingroup$ Thanks, can you please explain why ab - c is not an element of $R^{2}$? $\endgroup$– NewOct 11, 2011 at 16:09
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2$\begingroup$ 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? $\endgroup$– NewOct 11, 2011 at 16:11
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