Geodesic
Maximal ideals in semirings of continuous functions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 923-937 Cet article a éte moissonné depuis la source Math-Net.Ru

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The author investigates the conditions on a topological space $X$ and a topological semiring $S$ of the existence of a canonical homeomorphism between the maximal ideal space of the semiring $C(X,S)$ and the Tikhonov product of $X$ and the maximal ideal space of the semiring $S$. The generalized zero sets and the properties of continuous function semirings are considered. An analog of Gelfand–Kolmogorov theorem is obtained for maximal ideals of semirings of continuous functions with values in topological semiskewfields. 
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V. I. Varankina. Maximal ideals in semirings of continuous functions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 923-937. http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a5/

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

[2] Kaplansky I., “Topological rings”, Amer. J. Math., 69 (1947), 153–183 | DOI | MR | Zbl

[3] Slowikowski W., Zawadowski A., “A generalization of maximal ideals method of Stone and Gelfand”, Fund. Math., 42:2 (1955), 215–231 | MR | Zbl

[4] Vechtomov E. M., “K teoreme Gelfanda–Kolmogorova o maksimalnykh idealakh kolets nepreryvnykh funktsii”, Uspekhi matem. nauk, 47:5 (1992), 171–172 | MR | Zbl

[5] Hery W. J., “Maximal ideals in algebras of topological algebra valued functions”, Pacif. J. Math., 65:2 (1976), 365–373 | MR | Zbl

[6] Kalmutskii L. I., “Polukoltsa funktsii i kharakteristika $T_1$-prostranstv”, DAN BSSR, 30:11 (1986), 972–974 | MR

[7] Gillman L., Jerisan M., Rings of continuous functions, Springer–Verlag, N. Y., 1976 | MR | Zbl

[8] Banaschewski B., “Über nulldimensionale Räume”, Math. Nachr., 13:3–4 (1955), 129–140 | DOI | MR | Zbl

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