Prime group graded rings with applications to partial crossed products and Leavitt path algebras

We generalize a classical result by Passman on primeness of unital strongly group graded rings to the class of nearly epsilon-strongly group graded rings which are not necessarily unital. Using this result, we obtain (i) a characterization of prime sunital strongly group graded rings, and, in particular, of infinite matrix rings and of group rings over s-unital rings, thereby generalizing a well-known result by Connell; (ii) characterizations of prime s-unital partial skew group rings and of prime unital partial crossed products; (iii) a generalization of the well-known characterizations of prime Leavitt path algebras, by Larki and by Abrams-Bell-Rangaswamy. (c) 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).