Geodesic
Isomorphisms of semirings of continuous nonnegative functions with max-addition and isomorphisms of lattices of their subalgebras
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 318-337.

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Let $\mathbb{R}^{\vee}_+$ be the semifield with zero of nonnegative real numbers with operations of max-addition and multiplication and $C^{\vee}(X)$ be the semiring of continuous $\mathbb{R}^{\vee}_+$-valued functions on an arbitrary topological space $X$ with pointwise operation max-addition and multiplication. We call a subset $A\subseteq C^{\vee}(X)$ a subalgebra of the semiring $C^{\vee}(X)$ if $f\vee g,$ $fg,$ $rf\in A$ for any $f, g\in A$ and $r\in\mathbb{R}^{\vee}_+.$ For arbitrary topological spaces $X$ and $Y,$ we describe isomorphisms of the lattices of subalgebras (subalgebras with unity) of the semirings $C^{\vee}(X)$ and $C^{\vee}(Y).$
Keywords: semirings of continuous functions, lattice of subalgebras, Hewitt space, max-addition.
Mots-clés : subalgebra, isomorphism 
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V. V. Sidorov. Isomorphisms of semirings of continuous nonnegative functions with max-addition and isomorphisms of lattices of their subalgebras. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 318-337. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a6/

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