On conditions for semirings to induce compact information algebras

In this paper, we study the relationship between ordering structures on semirings and semiring-induced valuation algebras. We show that a semiring-induced valuation algebra is a complete (resp. continuous) lattice if and only if the semiring is complete (resp. continuous) lattice with respect to the reverse order relation on semirings. Furthermore, a semiring-induced information algebra is compact, if the dual of the semiring is an algebraic lattice.