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This article is cited in 2 scientific papers (total 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.
Received February 8, 2017, published September 22, 2017
Citation:
V. V. Chermnykh, O. V. Chermnykh, “Functional representations of lattice-ordered semirings”, Sib. Èlektron. Mat. Izv., 14 (2017), 946–971
Linking options:
https://www.mathnet.ru/eng/semr837 https://www.mathnet.ru/eng/semr/v14/p946
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