The Generalized Translation Dual of a Semifield

In this paper, elaborating on the link between semifields of dimension n over their left nucleus and \({\mathbb{F}s}\)-linear sets of rank en disjoint from the secant variety \({\Omega(\mathcal{S}_{n,n})}\) of the Segre variety \({\mathcal{S}_{n,n}}\) of \({PG(n^2-1, q), q=s^e}\), we extend some operations on semifield whose definition relies on dualising the relevant linear set.