Of, or relating to isotopes

Of two presemifields \mathbb{S} and \mathbb{S}' of characteristic p, when there exists three linear maps g_1, g_2, and g_3 from \mathbb{S} to \mathbb{S}' such that g_1(x\cdot y) = g_2(x) \circ g_3(y) for all x,y \in \mathbb{S}.