Geodesic
The principal kernels of semifields of continuous positive functions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 4, pp. 87-107
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This work is devoted to the research of kernel lattices of semifields of continuous positive functions defined on some topological space. It is established that they are lattices with pseudo-complement. New characterizations of the following properties of topological spaces are obtained in terms of kernels, predominantly principal kernels, and semifields of continuous functions: to be an F-space, to be a P-space, basical and extremal disconnectedness, pseudo-compactness, and finiteness. 
@article{FPM_2008_14_4_a5,
     author = {E. M. Vechtomov and D. V. Chuprakov},
     title = {The principal kernels of semifields of continuous positive functions},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {87--107},
     year = {2008},
     volume = {14},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a5/}
}
TY  - JOUR
AU  - E. M. Vechtomov
AU  - D. V. Chuprakov
TI  - The principal kernels of semifields of continuous positive functions
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2008
SP  - 87
EP  - 107
VL  - 14
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a5/
LA  - ru
ID  - FPM_2008_14_4_a5
ER  - 
%0 Journal Article
%A E. M. Vechtomov
%A D. V. Chuprakov
%T The principal kernels of semifields of continuous positive functions
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2008
%P 87-107
%V 14
%N 4
%U http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a5/
%G ru
%F FPM_2008_14_4_a5
E. M. Vechtomov; D. V. Chuprakov. The principal kernels of semifields of continuous positive functions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 4, pp. 87-107. http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a5/

[1] Birkgof G., Teoriya reshëtok, Nauka, M., 1984 | MR

[2] Varankina V. I., “Maksimalnye idealy v polukoltsakh nepreryvnykh funktsii”, Fundament. i prikl. mat., 1:4 (1995), 923–937 | MR | Zbl

[3] Varankina V. I., Vechtomov E. M., Semënova I. A., “Polukoltsa nepreryvnykh neotritsatelnykh funktsii: delimost, idealy, kongruentsii”, Fundament. i prikl. mat., 4:2 (1998), 493–510 | MR | Zbl

[4] Vechtomov E. M., “Distributivnye koltsa nepreryvnykh funktsii i F-prostranstva”, Mat. zametki, 34:3 (1983), 321–332 | MR | Zbl

[5] Vechtomov E. M., “Voprosy opredelyaemosti topologicheskikh prostranstv algebraicheskimi sistemami nepreryvnykh funktsii”, Itogi nauki i tekhniki. Algebra. Topologiya. Geometriya, 28, VINITI, M., 1990, 3–46 | MR | Zbl

[6] Vechtomov E. M., “Koltsa nepreryvnykh funktsii. Algebraicheskie aspekty”, Itogi nauki i tekhniki. Algebra. Topologiya. Geometriya, 29, VINITI, M., 1991, 119–191 | MR | Zbl

[7] Vechtomov E. M., Koltsa nepreryvnykh funktsii na topologicheskikh prostranstvakh. Izbrannye temy, MGPU im. V. I. Lenina, M., 1992 | MR

[8] Vechtomov E. M., Funktsionalnye predstavleniya kolets, MGPU im. V. I. Lenina, M., 1993 | MR

[9] Vechtomov E. M., “Polukoltsa nepreryvnykh otobrazhenii”, Vestn. Vyatsk. gos. guman. un-ta, 2004, no. 10, 57–64

[10] Vechtomov E. M., Cheranëva A. V., “K teorii polutel”, Uspekhi mat. nauk, 63:2 (2008), 161–162 | MR | Zbl

[11] Vechtomov E. M., Chuprakov D. V., “Kongruentsii na polukoltsakh nepreryvnykh funktsii i F-prostranstva”, Vestn. Syktyvkarsk. un-ta. Ser. 1. Matem., mekh., inform., 8 (2008), 15–26 | MR

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

[13] Podlevskikh M. N., “Zamknutye kongruentsii na polukoltsakh nepreryvnykh funktsii”, Fundament. i prikl. mat., 5:3 (1999), 947–952 | MR | Zbl

[14] Polin S. V., “Prostye polutela i polupolya”, Sib. mat. zhurn., 15:1 (1974), 90–101 | MR | Zbl

[15] Semënova I. A., “Maksimalnye kongruentsii na polupole nepreryvnykh polozhitelnykh funktsii”, Fundament. i prikl. mat., 6:1 (2000), 305–310 | MR | Zbl

[16] Shirokov D. V., “Usloviya distributivnosti reshëtki kongruentsii polupolya nepreryvnykh polozhitelnykh funktsii”, Vestn. Vyatsk. gos. guman. un-ta, 2003, no. 8, 137–140

[17] Acharyya S. K., Chattopalhyay K. S., Ray G. G., “Hemirings, congruences and the Stone–Čech compactification”, Simon Stevin, 67 (1993), 21–35 | MR | Zbl

[18] Acharyya S. K., Chattopalhyay K. S., Ray G. G., “Hemirings, congruences and the Hewitt real compactification”, Bull. Belg. Math. Soc., 2:1 (1995), 47–58 | MR | Zbl

[19] Artamonova I. I., Chermnykh V. V., Mikhalev A. V., Varankina V. I., Vechtomov E. M., “Semirings: Sheaves and continuous functions”, Semigroups with Applications, Including Semigroup Rings, Int. Conf. in Honour of E. S. Lyapin (St.-Petersburg, Russia, June 19–30, 1995), Severny Ochag, Saint-Petersburg, 1999, 23–58 | Zbl

[20] Gillman L., Henriksen M., “Concerning rings of continuous functions”, Trans. Amer. Math. Soc., 77:2 (1954), 340–362 | DOI | MR | Zbl

[21] Gillman L., Henriksen M., “Rings of continuous functions in which every finitely generated ideal is principal”, Trans. Amer. Math. Soc., 82:2 (1956), 366–391 | DOI | MR | Zbl

[22] Gillman L., Jerison M., Rings of continuous functions, Springer, New York, 1976 | MR | Zbl

[23] Golan J. F., Semirings and their applications, Kluwer Academic, Dordrecht, 1999 | MR

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

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

[26] Pierce R. S., “Rings of integer-valued continuous functions”, Trans. Amer. Math. Soc., 100:3 (1961), 371–394 | DOI | MR | Zbl

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

[28] Stone M., “Applications of the theory of Boolean rings to general topology”, Trans. Amer. Math. Soc., 41:3 (1937), 375–481 | DOI | MR | Zbl

[29] Vechtomov E. M., “Rings and sheaves”, J. Math. Sci., 74:1 (1995), 749–798 | DOI | MR | Zbl

[30] Vechtomov E. M., “Rings of continuous functions with values in a topological division ring”, J. Math. Sci., 78:6 (1996), 702–753 | DOI | MR | Zbl