Path algebras over arbitrary graphs have perfection and finiteness properties characterized by graph geometry, with semiprime ones decomposing into simple/prime/primitive summands and noetherian ones reducing to triangular matrix algebras or cycle sums plus fields.
Corrales García, Dolores Martín Barquero, Cánd ido Martín González, Mercedes Siles Molina, and José F
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Algebraic characterisations of path algebras
Path algebras over arbitrary graphs have perfection and finiteness properties characterized by graph geometry, with semiprime ones decomposing into simple/prime/primitive summands and noetherian ones reducing to triangular matrix algebras or cycle sums plus fields.