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Sib. Èlektron. Mat. Izv., 2017, Volume 14, Pages 946–971 (Mi semr837)  

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: latticeľordered semiring, functional semiring, sheaf representation.

DOI: https://doi.org/10.17377/semi.2017.14.080

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Bibliographic databases:

UDC: 512.55
MSC: 16Y60
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

Citation in format AMSBIB
\Bibitem{CheChe17}
\by V.~V.~Chermnykh, O.~V.~Chermnykh
\paper Functional representations of lattice-ordered semirings
\jour Sib. \`Elektron. Mat. Izv.
\yr 2017
\vol 14
\pages 946--971
\mathnet{http://mi.mathnet.ru/semr837}
\crossref{https://doi.org/10.17377/semi.2017.14.080}


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    This publication is cited in the following articles:
    1. O. V. Chermnykh, “Funktsionalnye predstavleniya reshetochno uporyadochennykh polukolets. II”, Sib. elektron. matem. izv., 15 (2018), 677–684  mathnet  crossref
    2. V. V. Chermnykh, O. V. Chermnykh, “Funktsionalnye predstavleniya reshetochno uporyadochennykh polukolets. III”, Tr. IMM UrO RAN, 26, no. 3, 2020, 235–248  mathnet  crossref  elib
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