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 Mat. Sb. (N.S.), 1988, Volume 136(178), Number 3(7), Pages 361–376 (Mi msb1747)

The fundamental theorem of Galois theory

G. Z. Dzhanelidze

Abstract: 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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English version:
Mathematics of the USSR-Sbornik, 1989, 64:2, 359–374

Bibliographic databases:

UDC: 512.58+512.7+512.66
MSC: Primary 13B05, 16A74; Secondary 12F10, 18A25, 18B40

Citation: G. Z. Dzhanelidze, “The fundamental theorem of Galois theory”, Mat. Sb. (N.S.), 136(178):3(7) (1988), 361–376; Math. USSR-Sb., 64:2 (1989), 359–374

Citation in format AMSBIB
\Bibitem{Dzh88} \by G.~Z.~Dzhanelidze \paper The fundamental theorem of Galois theory \jour Mat. Sb. (N.S.) \yr 1988 \vol 136(178) \issue 3(7) \pages 361--376 \mathnet{http://mi.mathnet.ru/msb1747} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=959487} \zmath{https://zbmath.org/?q=an:0677.18003|0653.18002} \transl \jour Math. USSR-Sb. \yr 1989 \vol 64 \issue 2 \pages 359--374 \crossref{https://doi.org/10.1070/SM1989v064n02ABEH003313} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. G. Janelidze, G.M. Kelly, “Galois theory and a general notion of central extension”, Journal of Pure and Applied Algebra, 97:2 (1994), 135
2. George Janelidze, László Márki, Walter Tholen, “Locally semisimple coverings”, Journal of Pure and Applied Algebra, 128:3 (1998), 281
3. Michael Müger, “Galois Theory for Braided Tensor Categories and the Modular Closure”, Advances in Mathematics, 150:2 (2000), 151
4. George Janelidze, “Galois Groups, Abstract Commutators, and Hopf Formula”, Appl Categor Struct, 2007
5. Dali Zangurashvili, “Effective codescent morphisms, amalgamations and factorization systems”, Journal of Pure and Applied Algebra, 209:1 (2007), 255
6. George Janelidze, “Light morphisms for generalized -reflections”, Topology and its Applications, 156:12 (2009), 2109
7. S. H. Dalalyan, “Grothendieck’s extension of the fundamental theorem of galois theory in abstract categories”, J. Contemp. Mathemat. Anal, 46:1 (2011), 48
8. Dominique Bourn, Diana Rodelo, “Comprehensive factorization and -central extensions”, Journal of Pure and Applied Algebra, 2011
9. Marino Gran, Tomas Everaert, “Monotone-light factorisation systems and torsion theories”, Bulletin des Sciences Mathématiques, 2013
10. Tamar Janelidze-Gray, “Composites of Central Extensions Form a Relative Semi-Abelian Category”, Appl Categor Struct, 2013
11. M.M.anuel Clementino, Dirk Hofmann, Andrea Montoli, “Covering Morphisms in Categories of Relational Algebras”, Appl Categor Struct, 2013
12. Tomas Everaert, Marino Gran, “Protoadditive functors, derived torsion theories and homology”, Journal of Pure and Applied Algebra, 2014
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