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. 
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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/

[1] Vechtomov E. M., “Voprosy opredelyaemosti topologicheskikh prostranstv algebraicheskimi sistemami nepreryvnykh funktsii”, Itogi nauki i tekhn. Ser. Algebra. Topol. Geom., 28, 1990, 3–46 | MR | Zbl

[2] Vechtomov E. M., “Koltsa nepreryvnykh funktsii. Algebraicheskie aspekty”, Itogi nauki i tekhn. Ser. Algebra. Topol. Geom., 29, 1991, 119–191 | MR | Zbl

[3] Vechtomov E. M., “Reshëtka podalgebr kolets nepreryvnykh funktsii i khyuittovskie prostranstva”, Matem. zametki, 62:5 (1997), 687–693 | DOI | MR | Zbl

[4] Vechtomov E. M., Vvedenie v polukoltsa, VGPU, Kirov, 2000

[5] Vechtomov E. M., Sidorov V. V., “Izomorfizmy reshëtok podalgebr polukolets nepreryvnykh neotritsatelnykh funktsii”, Fundament. i prikl. matem., 16:3 (2010), 63–103 | MR

[6] Gelfand I. M., Kolmogorov A. N., “O koltsakh nepreryvnykh funktsii na topologicheskikh prostranstvakh”, DAN SSSR, 22:1 (1939), 11–15 | Zbl

[7] Grettser G., Obschaya teoriya reshëtok, Mir, M., 1982 | MR

[8] Engelking R., Obschaya topologiya, Mir, M., 1986 | MR

[9] Cabello Sánchez F., Cabello Sánchez J., Ercan Z., Önal S., “Memorandum on multiplicative bijections and order”, Semigroup Forum, 79 (2009), 193–209 | DOI | MR | Zbl

[10] Gillman L., Jerison M., Rings of Continuous Functions, Springer, New York, 1976 | MR | Zbl

[11] Golan J. F., Semirings and Their Applications, Kluwer Academic, Dordrecht, 1999 | MR | Zbl

[12] Hewitt E., “Rings of real-valued continuous functions”, Trans. Amer. Math. Soc., 64:1 (1948), 45–99 | DOI | MR | Zbl

[13] Marovt J., “Multiplicative bijections of $C(X,I)$”, Proc. Amer. Math. Soc., 134:4 (2005), 1065–1075 | DOI | MR