p-radical of a Semiring.

In our continuing endeavour towards establishing the theory of p-ideals [4, 5, 7] in semiring, we have introduced in [1], the idea of p-prime and p-semiprime ideals in semiring and some related results were established, including that the intersection of any class of p-prime ideals of a semiring is a p-semiprime ideal thereof. In the present paper we introduce the concept of p-radical of an ideal of a commutative semiring and establish the corresponding version of the famous Krull's theorem for this structure. Thereafter, defining the p-radical of a semiring and p-nilpotent elements of a semiring, we present some interrelations between them. [ABSTRACT FROM AUTHOR]