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Trudy Inst. Mat. i Mekh. UrO RAN, 2020, Volume 26, Number 3, Pages 235–248 (Mi timm1759)  

Functional representations of lattice-ordered semirings. III

V. V. Chermnykha, O. V. Chermnykhb

a Syktyvkar State University
b Vyatka State University

Abstract: Lattice-ordered semirings ($drl$-semirings) are considered. Compact sheaves of $drl$-semirings are defined and their characterization is obtained. The properties of compact sheaves are studied; in particular, the structure of irreducible and maximal $l$-ideals in the $drl$-semiring of sections of a compact sheaf is described. A compact sheaf of functional semirings ($f$-semirings) is described in terms of a continuous mapping of the irreducible (and maximal) spectrum of this sheaf onto a compact Hausdorff space. The paper also contains a proof that an $f$-semiring is Gelfand if and only if it is isomorphic to the semiring of all sections of a compact sheaf of $f$-semirings with a unique maximal ideal.

Keywords: lattice-ordered semiring, functional semiring, compact sheaf, Gelfand $f$-semiring.

DOI: https://doi.org/10.21538/0134-4889-2020-26-3-235-248

Full text: PDF file (240 kB)
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Bibliographic databases:

UDC: 512.25
MSC: 16Y60
Received: 07.04.2020
Revised: 23.04.2020
Accepted:11.05.2020

Citation: V. V. Chermnykh, O. V. Chermnykh, “Functional representations of lattice-ordered semirings. III”, Trudy Inst. Mat. i Mekh. UrO RAN, 26, no. 3, 2020, 235–248

Citation in format AMSBIB
\Bibitem{CheChe20}
\by V.~V.~Chermnykh, O.~V.~Chermnykh
\paper Functional representations of lattice-ordered semirings. III
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2020
\vol 26
\issue 3
\pages 235--248
\mathnet{http://mi.mathnet.ru/timm1759}
\crossref{https://doi.org/10.21538/0134-4889-2020-26-3-235-248}
\elib{https://elibrary.ru/item.asp?id=43893877}


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