Suppose one has a ring with two alternative multiplications, like "$\times$" and "$\cdot$". Each one rises a set of analytic functions that can be applied to the elements of the ring.
What notations are used to differentiate between functions built with one multiplication from the ones built with the other? For instance, like $\sin_\times(x)$ versus $\sin_\cdot(x)$ or are there other methods?
