This article is cited in 2 papers

Mathematical logic, algebra and number theory

Functional representations of lattice-ordered semirings

V. V. Chermnykh, O. V. Chermnykh

Vyatka state universite, Moskovskaya, 36, 610000, Kirov, Russia

Abstract: The paper is devoted to lattice-ordered semirings ($drl$-semirings) and their representations by sections of sheaves. We build two sheaves of $drl$-semirings. The first sheaf construction is generalization of Keimel sheaf of $l$-rings, the second sheaf is analogy of Lambek sheaf of abstract semirings. The classes of Gelfand, Rickart, biregular and strongly regular $f$-semirings are investigated in this paper. The main aim is to study sheaf representations of such algebras.

Keywords: lattice–ordered semiring, functional semiring, sheaf representation.

UDC: 512.55

MSC: 16Y60

Received February 8, 2017, published September 22, 2017

DOI: 10.17377/semi.2017.14.080

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