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

AbstractLet G be a group. In their study of G-graded rings R, Nǎstǎsescu 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 Nǎstǎsescu 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