Geodesic
Subalgebras in semirings of continuous partial real-valued functions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 24 (2022) no. 1, pp. 125-140
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This paper refers to the theory of semirings of continuous numerical functions, which has been developed within functional algebra. The object of the investigation is semirings $CP(X)$ of continuous partial functions on topological spaces $X$ with the values in the topological field $\mathbf{R}$ of real numbers. The subject of study is the subalgebras of semirings $CP(X)$. Some properties of the lattices $A(X)$ of all possible subalgebras and $A_1(X)$ of all subalgebras with identity are considered. The structure of atoms and preatoms in lattices $A_1(X)$ is clarified. This allowed us to solve the problem of the absolute determinability of $T_1$-spaces $X$ by each of the lattices $A_1(X)$ and $A_1(X)$. 
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E. M. Vechtomov; E. N. Lubyagina. Subalgebras in semirings of continuous partial real-valued functions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 24 (2022) no. 1, pp. 125-140. http://geodesic.mathdoc.fr/item/FPM_2022_24_1_a2/

[1] Vechtomov E. M., Lubyagina E. N., “Polukoltsa nepreryvnykh chastichnykh deistvitelnoznachnykh funktsii”, Proc. of the 48th Int. Youth School-Conference “Modern Problems in Mathematics and Its Applications” (Yekaterinburg, Russia, February 5–11, 2017), CEUR Workshop Proceedings, 1894, 20–29 | MR

[2] Vechtomov E. M., Lubyagina E. N., Sidorov V. V., Chuprakov D. V., Elementy funktsionalnoi algebry, ed. E. M. Vechtomov, Raduga-PRESS, Kirov, 2016

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

[4] Grettser G., Obschaya teoriya reshetok, Mir, M., 1982

[5] Sidorov V. V., “Izomorfizmy reshetok podalgebr polupolei nepreryvnykh polozhitelnykh funktsii”, Sib. matem. zhurn., 60:3 (2019), 676–694 | MR | Zbl

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

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

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

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

[10] Sidorov V. V., “Isomorphisms of semirings of continuous nonnegative functions and the lattices of their subalgebras”, Lobachevskii J. Math., 41:9 (2020), 1684–1692 | DOI | MR | Zbl