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1. (mathematics) Of two presemifields ${\displaystyle \mathbb {S} }$ and ${\displaystyle \mathbb {S} '}$ of characteristic ${\displaystyle p}$, when there exists three linear maps ${\displaystyle g_{1}}$, ${\displaystyle g_{2}}$, and ${\displaystyle g_{3}}$ from ${\displaystyle \mathbb {S} }$ to ${\displaystyle \mathbb {S} '}$ such that ${\displaystyle g_{1}(x\cdot y)=g_{2}(x)\circ g_{3}(y)}$ for all ${\displaystyle x,y\in \mathbb {S} }$.
2. (mathematics) 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· y) = g_2(x) ° g_3(y) for all x,y ∈ \mathbb{S}.