Morita Duality for the Rings of Generalized Power Series

Let A, B be associative rings with identity, and (S, ) a strictly totally ordered monoid which is also artinian and finitely generated. For any bimodule A M B , we show that the bimodule [[AS,]][MS,][[BS,]] defines a Morita duality if and only if A M B defines a Morita duality and A is left noetherian, B is right noetherian. As a corollary, it is shown that the ring [[A S,]] of generalized power series over A has a Morita duality if and only if A is a left noetherian ring with a Morita duality induced by a bimodule A M B such that B is right noetherian.