• A NOTE ON BOOLEAN TERNARY SEMIRINGS

Abstract

The main purpose of this note is to prove that a commutative Boolean ternary semiring of characteristic two is isomorphic to a Boolean ring. Further, we construct a ternary semiring (not necessarily commutative), provided a semiring with absorbing zero and some of their properties are obtained. Finally, the existence of a non-commutative Boolean ternary semiring which is not of characteristic two is illustrated.