Superdecomposable Complete Path Algebras
Can Hatipoğlu, Christian Lomp
Abstract
Generalizing the setting of the second author's work on indecomposable modules without nonzero hollow factors, we characterize quivers Q for which the dual algebra R of the path coalgebra of Q, equivalently the complete path algebra, has no nonzero uniform right ideals: this happens exactly when every vertex of Q can reach a vertex emitting at least two distinct arrows. Equivalently, the injective hull E(R) of the right regular module is superdecomposable. These conditions are also equivalent to the path coalgebra having no nonzero hollow factor modules as a left module over its dual algebra.
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