Geodesic
The fundamental theorem of Galois theory
Sbornik. Mathematics, Tome 64 (1989) no. 2, pp. 359-374 Cet article a éte moissonné depuis la source Math-Net.Ru

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For arbitrary categories $C$ and $X$ and an arbitrary functor $I\colon C\to X$ the author introduces the notion of an $I$-normal object and proves a general type of fundamental theorem of Galois theory for such objects. It is shown that the normal extensions of commutative rings and central extensions of multi-operator groups are special cases of $I$-normal objects. Bibliography: 14 titles. 
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     title = {The fundamental theorem of {Galois} theory},
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G. Z. Dzhanelidze. The fundamental theorem of Galois theory. Sbornik. Mathematics, Tome 64 (1989) no. 2, pp. 359-374. http://geodesic.mathdoc.fr/item/SM_1989_64_2_a4/

[1] Barr M., “Abstract Galois theory”, JPAAA, 19 (1980), 21–42 | MR | Zbl

[2] Grothendieck A., Séminaire de Géométric Algébrique. I. Revêtements étale et groupe fondamental (1960/61), Springer, Heidelberg, 1971 | MR

[3] Magid A. R., The separable Galois theory of commutative rings, Marsel Dekker, New York, 1974 | MR

[4] Fröhlich A., “Baer-invariants of algebras”, Trans. AMS., 109 (1963), 221–244 | DOI | MR | Zbl

[5] Janelidze G., “A generalization of the theory of covering spaces”, Abstracts of the IV Internat. Conf. in Topology and its Applications, Dubrovnik, 1985

[6] Dzhanelidze G. Z., “Teorema Megida v kategoriyakh”, Soobsch. AN GSSR, 114:3 (1984), 477–500 | MR

[7] Barr M., “Abstract Galois Theory II”, JPAAA, 25 (1982), 227–247 | MR | Zbl

[8] Mac Lane S., Categories for the working mathematician, Springer, Berlin, 1971

[9] Jornstone P. T., Topos theory, Academic Press, New York, 1977 | MR

[10] Chase S. U., Sweedler M. E., Hopf algebras and Galois theory, Springer, Berlin, 1969 | MR | Zbl

[11] Pierce R. S., “Modules over commutative regular rings”, Mem. AMS, 70 (1967) | MR | Zbl

[12] Dzhanelidze G. Z., “Rasshireniya Galua kommutativnykh kolets, s pomoschyu prokonechnykh semeistv grupp”, Tr. MI AN GSSR, 74 (1983), 39–51 | MR

[13] Auslander M., Goldman O., “The Brauer group of a commutative ring”, Trans. AMS, 97 (1960), 367–409 | DOI | MR

[14] Chase S. U., Harrison D. K., Rosenberg A., “Galois theory and cohomology of commutative rings”, Mem. AMS, 52 (1965), 15–33 | MR | Zbl