Prime and primitive Kumjian–Pask algebras

Abstract

In this paper, prime as well as primitive Kumjian–Pask algebras [Formula: see text] of a row-finite [Formula: see text]-graph [Formula: see text] over a unital commutative ring [Formula: see text] are completely characterized in graph-theoretic and algebraic terms. By applying quotient [Formula: see text]-graphs, these results describe prime and primitive graded basic ideals of Kumjian–Pask algebras. In particular, when [Formula: see text] is strongly aperiodic and [Formula: see text] is a field, all prime and primitive ideals of a Kumjian–Pask algebra [Formula: see text] are determined.