Functional representations of lattice-ordered semirings. III
V. V. Chermnykha, O. V. Chermnykhb
a Syktyvkar State University
b Vyatka State University
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.
lattice-ordered semiring, functional semiring, compact sheaf, Gelfand $f$-semiring.
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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
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\by V.~V.~Chermnykh, O.~V.~Chermnykh
\paper Functional representations of lattice-ordered semirings. III
\serial Trudy Inst. Mat. i Mekh. UrO RAN
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