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ABSTRACT. Certain types of ring congruences on an additive inverse semiring are characterized with the help of full k-ideals. It is also shown that the set of all full k-ideals of an additively inverse semiring in which addition is commutative forms a complete lattice which is also modular. KEY WORDS AND PHRASES. Semiring, inverse semiring, k-ideals and ring congruence. 1991 AMS SUBJECT CLASSIFICATION CODE. 16A-78. 1. PRELIMINARIES. A semiring is a system consisting of a non-empty set S together with two binary operations on S called addition and multiplication (denoted in the usual manner) such that (i) S together with addition is a semigroup; (ii) S together with multiplication is a semigroup; and (iii) a(b + c) ab + ac and (a + b)c ac + bc for all a,b,c _ S. A semiring S is said to be a,dditively commutative if a + b b + a for all a,b E S. A left (right) ideal of a semiring S is non-empty subset I of S such that i) a + b E I for all a,b _ I; an