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Lobachevskii Journal of Mathematics

, Volume 40, Issue 1, pp 90–100 | Cite as

Determinability of Semirings of Continuous Nonnegative Functions with Max-Plus by the Lattices of Their Subalgebras

  • V. V. SidorovEmail author
Article
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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 fg, fg, rfA for any f, gA, \(r \in \mathbb{R}_+^\vee\). 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)).

Keywords and phrases

semiring of continuous functions subalgebra lattice of subalgebras isomorphism Hewitt space max-addition 

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Vyatka State UniversityKirovRussia

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