Horn formuls in pierce chains of semirings

This paper describes construction of a pierce chain of congruences of a semiring — analogue of pierce chains of ideals of a ring, necessary definitions are introduced: a ring of central supplemented idempotents, a congruence of Peirce, a pierce sheaf of semirings, a pierce representation of semirings, a pierce chain of congruences, a horn formula. The basic result of paper is the theorem 1 about equivalence of realizability of horn formulas without negation on a semiring and its factors, additional result is an application of the theorem 1 for the proof of "transposition" of properties of a semiring of a Bezout on its factors and is inverse.