Geodesic
Partial Hopf--Galois theory
Algebra i logika, Tome 61 (2022) no. 5, pp. 571-599.

Voir la notice de l'article provenant de la source Math-Net.Ru

A partial Hopf–Galois theory is developed for partial $H$-module algebras, and we recover analogs of classical results for Hopf algebras.
Keywords: Hopf–Galois theory, partial action, Hopf algebra, Frobenius extension. 
@article{AL_2022_61_5_a3,
     author = {F. Castro and D. Freitas and A. Paques and G. Quadros and T. Tamusiunas},
     title = {Partial {Hopf--Galois} theory},
     journal = {Algebra i logika},
     pages = {571--599},
     publisher = {mathdoc},
     volume = {61},
     number = {5},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2022_61_5_a3/}
}
TY  - JOUR
AU  - F. Castro
AU  - D. Freitas
AU  - A. Paques
AU  - G. Quadros
AU  - T. Tamusiunas
TI  - Partial Hopf--Galois theory
JO  - Algebra i logika
PY  - 2022
SP  - 571
EP  - 599
VL  - 61
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2022_61_5_a3/
LA  - ru
ID  - AL_2022_61_5_a3
ER  - 
%0 Journal Article
%A F. Castro
%A D. Freitas
%A A. Paques
%A G. Quadros
%A T. Tamusiunas
%T Partial Hopf--Galois theory
%J Algebra i logika
%D 2022
%P 571-599
%V 61
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2022_61_5_a3/
%G ru
%F AL_2022_61_5_a3
F. Castro; D. Freitas; A. Paques; G. Quadros; T. Tamusiunas. Partial Hopf--Galois theory. Algebra i logika, Tome 61 (2022) no. 5, pp. 571-599. http://geodesic.mathdoc.fr/item/AL_2022_61_5_a3/

[1] S. Caenepeel, K. Janssen, “Partial (co)actions of Hopf algebras and partial Hopf–Galois theory”, Commun. Algebra, 36:8 (2008), 2923–2946 | DOI | MR | Zbl

[2] S. Montgomery, “Hopf algebras and their actions on rings”, Conference on Hopf algebras and their actions on rings (DePaul Univ., Chicago, USA, August 10-14, 1992), Reg. Conf. Ser. Math., 82, Am. Math. Soc., Providence, RI, 1993 | MR

[3] F. Castro, A. Paques, G. Quadros, A. Sant'Ana, “Partial actions of weak Hopf algebras: smash product, globalization and Morita theory”, J. Pure Appl. Algebra, 219:12 (2015), 5511–5538 | DOI | MR | Zbl

[4] C. Lomp, “Integrals in Hopf algebras over rings”, Commun. Algebra, 32:12 (2004), 4687–4711 | DOI | MR | Zbl

[5] F. Castro, G. Quadros, “Globalizations for partial (co)actions on coalgebras”, Algebra Discrete Math., 27:2 (2019), 212–242 | MR | Zbl

[6] E. Batista, J. Vercruysse, “Dual constructions for partial actions of Hopf algebras”, J. Pure Appl. Algebra, 220:2 (2016), 518–559 | DOI | MR | Zbl

[7] M. M. S. Alves, E. Batista, “Partial Hopf actions, partial invariants and a Morita context”, Algebra Discrete Math., 2009, no. 3, 1–19 | MR

[8] R. Wisbauer, Foundations of module and ring theory. A handbook for study and research, Algebra, Log. Appl., 3, Gordon and Breach Sci. Publ., Philadelphia etc., 1991 | MR | Zbl

[9] S. U. Chase, M. E. Sweedler, Hopf algebras and Galois theory, Lect. Notes Math., 97, Springer-Verlag, Berlin-Heidelberg-New York, 1969 | DOI | MR | Zbl