Geodesic
Horn formuls in pierce chains of semirings
Čebyševskij sbornik, Tome 14 (2013) no. 4, pp. 159-166.

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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.
Keywords: a semiring, a pierce representation of semirings, a central supplemented idempotent of a semiring, a pierce chain of congruences of a semiring, a horn formula without negation, a semiring of a Bezout. 
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R. V. Markov. Horn formuls in pierce chains of semirings. Čebyševskij sbornik, Tome 14 (2013) no. 4, pp. 159-166. http://geodesic.mathdoc.fr/item/CHEB_2013_14_4_a13/

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