A ternary partial semiring is a system consisting of an infinitary partial addition and a ternary multiplication satisfying a set of axioms. The set of nonpositive real numbers with respect to Σ, defined for countable support families of elements which are convergent and the usual ternary multiplication is a ternary partial semiring. In this paper, the notions of ternary partial semi-integral domain, ternary partial division semiring and ternary partial semifield are introduced. An equivalent condition for a commutative complete ternary partial semiring to be a ternary partial semifield is obtained.