2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69387We obtain that the global dimensions of $R$ and the crossed product $R # _σH$ are the same; meantime, their weak dimensions are also the same, when $H$ is finite-dimensional semisimple and cosemisimple Hopf algebra.13pageQuantum AlgebraRings and Algebras16w30text