Right Gaussian rings and skew power series rings

We introduce a class of rings we call right Gaussian rings, defined by the property that for any two polynomials f, g over the ring R, the right ideal of R generated by the coefficients of the product fg coincides with the product of the right ideals generated by the coefficients of f and of g, respectively. Prüfer domains are precisely commutative domains belonging to this new class of rings. In this paper we study the connections between right Gaussian rings and the classes of Armendariz rings and rings whose right ideals form a distributive lattice. We characterize skew power series rings (ordinary as well as generalized) that are right Gaussian, extending to the noncommutative case a well-known result by Anderson and Camillo. We also study quotient rings of right Gaussian rings.