Unit elements in the path algebra of an acyclic quiver. (English) Zbl 1493.16040
Summary: We investigate the algebraic properties of a particular non- commutative algebra, the path algebra, associated with a quiver. Quiver was initially introduced by Peter Gabriel. In this paper, we obtain a characterization for the invertibility of an element in the path algebra of an acyclic quiver. The study is an extension of the invertibility condition in a unique path quiver to acyclic quivers.
MSC:
| 16U60 | Units, groups of units (associative rings and algebras) |
| 16S99 | Associative rings and algebras arising under various constructions |
References:
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