Abstract
Let KQ be a path algebra, where Q is a finite quiver and K is a field. We study KQ/C where C is the two-sided ideal in KQ generated by all differences of parallel paths in Q. We show that KQ/C is always finite dimensional and its global dimension is finite. Furthermore, we prove that KQ/C is Morita equivalent to an incidence algebra.The paper starts with a more general setting, where KQ is replaced by KQ/I with I a two-sided ideal in KQ.
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