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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 677–684 (Mi semr944)  

This article is cited in 1 scientific paper (total in 1 paper)

Mathematical logic, algebra and number theory

Functional representations of lattice-ordered semirings. II

O. V. Chermnykh

Vyatka state universite, Moskovskaya, 36, 610000, Kirov, Russia

Abstract: The article considers the lattice-ordered semirings ($drl$-semirings). Two sheaves of $drl$-semirings are constructed. The first sheaf is based on prime spectrum of $l$-ideals. The idea of construction is close to the well-known sheaf of germs of continuous functions. The second sheaf resembles Pierce's sheaf of abstract rings or semirings. Its basis space is Boolean space of maximal ideals of the lattice of complemented $l$-ideals from $drl$-semiring. The main results are theorems on representations of an $l$-semiprime and an arbitrary $drl$-semirings by sections of corresponding sheaves.

Keywords: lattice-ordered semiring, sheaf, sheaf representation.

DOI: https://doi.org/10.17377/semi.2018.15.053

Full text: PDF file (149 kB)
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Bibliographic databases:

UDC: 512.25
MSC: 16Y60
Received April 1, 2018, published June 1, 2018

Citation: O. V. Chermnykh, “Functional representations of lattice-ordered semirings. II”, Sib. Èlektron. Mat. Izv., 15 (2018), 677–684

Citation in format AMSBIB
\Bibitem{Che18}
\by O.~V.~Chermnykh
\paper Functional representations of lattice-ordered semirings. II
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 677--684
\mathnet{http://mi.mathnet.ru/semr944}
\crossref{https://doi.org/10.17377/semi.2018.15.053}


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    This publication is cited in the following articles:
    1. 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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