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Functional representations of lattice-ordered semirings. (Russian. English summary) Zbl 1377.16042
Summary: 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.

MSC:
16Y60 Semirings
06B75 Generalizations of lattices
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