Geodesic
Functional representations of lattice-ordered semirings
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 946-971

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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. 
@article{SEMR_2017_14_a26,
     author = {V. V. Chermnykh and O. V. Chermnykh},
     title = {Functional representations of lattice-ordered semirings},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {946--971},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a26/}
}
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V. V. Chermnykh; O. V. Chermnykh. Functional representations of lattice-ordered semirings. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 946-971. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a26/