Abstract: ∶We define a sublattice of the lattice of congruence of a quasidistributive lattice S=［D;Sα］of semirings with multiplication identical elements . We also prove that such a sublattice is isomorphic to a sublattice of the direct product of lattice of congruence of Sα=［α∈D］. We further demonstrate the congruence of a quasidistributive lattice S=［D;Sα］ of inverse semirings with multiplication identical elements by congruence pairs.

Key words: distributive lattice, quasidistributive lattice, congruence pair, semiring, lattice of congruence on a semiring