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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.
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
Linking options:
https://www.mathnet.ru/eng/timm1759 https://www.mathnet.ru/eng/timm/v26/i3/p235
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Abstract page: | 234 | Full-text PDF : | 38 | References: | 34 | First page: | 4 |
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