Variations on the smash product with applications to group-graded rings Original Research Article

Let G be a group. In their study of G-graded rings R, Nimagestimagesescu et al. (1990) introduced the algebra R # A and the module category (G, A, R)-gr, for a finite G-set A. These extend older concepts where A = G. This paper shows how the context of Nimagestimagesescu et al. (1990) is generalized most naturally to comodule algebras for a bialgebra. Also some of their results are derived as special cases of the more general theory. The considered subjects include crossed products. The naturality of the generalization underlines the known fact that many interesting questions on group-graded rings are, in fact, Hopf algebra theoretic.