  We determine the Seiberg-Witten-Floer homology groups of the three-manifold
which is the product of a surface of genus $g \geq 1$ times the circle,
together with its ring structure, for spin-c structures which are non-trivial
on the three-manifold. We give applications to computing Seiberg-Witten
invariants of four-manifolds which are connected sums along surfaces and also
we reprove the higher type adjunction inequalities previously obtained by
Oszv\'ath and Szab\'o.
