L-R-crossed products

Given an associative algebra H, a linear space U and some linear maps J, T, γ, ηsatisfying some axioms, we define an associative algebra structure on U\otimes H, called an L-R-crossed product. This contains as particular cases some previous constructions, such as the (iterated) Brzezinski crossed product and the L-R-smash product over quasi-bialgebras.