Geodesic
Isomorphisms of lattices of subalgebras of semirings of continuous nonnegative functions with the max-plus
Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 6, pp. 153-189

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Isomorphisms $\varphi$ of semirings $C^\vee(X)$ of continuous nonnegative functions over an arbitrary Hewitt space $X$ with the condition $\varphi(\mathbb R^+)=\mathbb R^+$ are characterized in this work. It is proved that any isomorphism of lattices of all subalgebras of semirings $C^\vee(X)$ and $C^\vee(Y)$ is induced by a unique isomorphism of semirings excepting the case of one- and two-point Tychonovization of spaces. 
@article{FPM_2014_19_6_a7,
     author = {V. V. Sidorov},
     title = {Isomorphisms of lattices of subalgebras of semirings of continuous nonnegative functions with the max-plus},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {153--189},
     publisher = {mathdoc},
     volume = {19},
     number = {6},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2014_19_6_a7/}
}
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V. V. Sidorov. Isomorphisms of lattices of subalgebras of semirings of continuous nonnegative functions with the max-plus. Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 6, pp. 153-189. http://geodesic.mathdoc.fr/item/FPM_2014_19_6_a7/