On Bezout and distributive generalized power series rings

AbstractIn this paper we give sufficient and necessary conditions on a strongly regular ring of coefficients R and a monoid of nonnegative exponents S such that the generalized power series ring R〚S〛 is right Bezout. It is shown that all such generalized power series rings are right distributive. We also study when a generalized power series ring over a von Neumann regular ring has weak dimension less than or equal to one