matrices $X$, $Y$ are of different size, the effects of the characteristic polynomial are different in the two cases.

Quantum mechanically, the moduli spaces agree. After removing the subspaces of moduli space corresponding to unstable vacua we find, rather remarkably, the same number of components on both sides, with the same physical properties. Some of these properties will be investigated below.

Duality suggests a natural candidate for the quantum deformation of the chiral rings in the two theories. It is very natural to add to the classical relations coming from the equation of motion and the characteristic polynomial in the electric theory an additional set of relations following from the [*magnetic*]{} characteristic polynomial using the duality map . These relations would be described as quantum strong coupling effects in the electric theory (we will see that they are trivial when the electric theory is weakly coupled), while in the magnetic language they correspond to classical ‘trivial’ relations following from compositeness of $\Tr Y^j$. Similarly, the magnetic chiral ring is modified by quantum relations obtained via the duality map from the electric characteristic polynomial. One of our goals in this paper will be to establish that the quantum modification of the 