  It is shown that the K-theory of every noetherian base scheme of finite Krull
dimension is represented by a strict ring object in the setting of motivic
stable homotopy theory. The adjective `strict' is used to distinguish between
the type of ring structure we construct and one which is valid only up to
homotopy. Both the categories of motivic functors and motivic symmetric spectra
furnish convenient frameworks for constructing the ring models. Analogous
topological results follow by running the same type of arguments as in the
motivic setting.
