# Hereditary algebras as quotient algebras

This is the first time I post a question on MO, so I'm shy a liite bit. Can you give a "non-trivial" example of a finite dimensional hereditary algebra which is quotient of an infinite dimensional algebra ? By "non-trivial" I mean not by killing loops in the path algebra of some quiver, for example $k[X_1] \times\ldots \times k[X_n]/((X_1)\times\ldots\times (X_n))$.

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