In this paper, we study the necessary and sufficient conditions for the partial crossed product to be a fully weakly prime ring. Moreover, we give a description of the prime radical of the partial crossed product when the base ring is a fully weakly prime ring.
Wagner Cortes. Marlon Soares. "Partial crossed products and fully weakly prime rings." Rocky Mountain J. Math. 46 (4) 1107 - 1139, 2016. https://doi.org/10.1216/RMJ-2016-46-4-1107