Narrow Results

In this paper, we introduce the notion of prime hyperideals and maximal hyperideals in ternary hypersemirings and we study some of their properties. We construct a ternary semiring $P_{\circ }(S)$, corresponding to a strongly distributive ternary hypersemiring $S$ and obtain various results among them. We also establish an inclusion preserving bijection between the set of all prime hyperideals of $S$ and collection of all prime total k-ideals of $P_{\circ }(S)$.