\mathcal P-kernel normal system of an additive \mathcal P-regular semiring

\mathcal P-regular semigroups are an important class of semigroups. Sen described the congruence on a \mathcal P-regular semigroup by means of a \mathcal P-kernel normal system. In this paper we consider the additive \mathcal P-regular semiring and discuss the \mathcal P-kernel normal system of the additive \mathcal P-regular semiring. We prove that every congruence on this kind of semiring can induce a \mathcal P-kernel normal system, and every \mathcal P-kernel normal system uniquely determines a congruence. In the end we illustrate a \mathcal P-kernel normal system of an additive \mathcal P-regular semiring whose \overset+C-set is a semi-ideal.