Determinability of Semirings of Continuous Nonnegative Functions with Max-Plus by the Lattices of Their Subalgebras
- Authors: Sidorov V.V.1
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Affiliations:
- Vyatka State University
- Issue: Vol 40, No 1 (2019)
- Pages: 90-100
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/203820
- DOI: https://doi.org/10.1134/S1995080219010128
- ID: 203820
Cite item
Abstract
Denote by \(\mathbb{R}_+^\vee\) the semifield with zero of nonnegative real numbers with operations of max-addition and multiplication. Let X be a topological space and C∨(X) be the semiring of continuous nonnegative functions on X with pointwise operation max-addition and multiplication of functions. By a subalgebra we mean a nonempty subset A of C∨(X) such that f ∨ g, fg, rf ∈ A for any f, g ∈ A, \(r \in \mathbb{R}_+^\vee\). We consider the lattice \(\mathbb{A}\)(C∨(X)) of subalgebras of the semiring C∨(X) and its sublattice \(\mathbb{A}_1\)(C∨(X)) of subalgebras with unity. The main result of the paper is the proof of the definability of the semiring C∨(X) both by the lattice \(\mathbb{A}\)(C∨(X)) and by its sublattice \(\mathbb{A}_1\)(C∨(X)).
About the authors
V. V. Sidorov
Vyatka State University
Author for correspondence.
Email: sedoy_vadim@mail.ru
Russian Federation, Kirov, 610000