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On the Galois Correspondence Theorem in Separable Hopf Galois Theory

Teresa Crespo, Anna Rio, and Montserrat Vela

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In this paper we present a reformulation of the Galois correspondence theorem of Hopf Galois theory in terms of groups carrying farther the description of Greither and Pareigis. We prove that the class of Hopf Galois extensions for which the Galois correspondence is bijective is larger than the class of almost classically Galois extensions but not equal to the whole class. We show as well that the image of the Galois correspondence does not determine the Hopf Galois structure.

Article information

Publ. Mat., Volume 60, Number 1 (2016), 221-234.

First available in Project Euclid: 22 December 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 12F10: Separable extensions, Galois theory
Secondary: 13B05: Galois theory 16T05: Hopf algebras and their applications [See also 16S40, 57T05]

Hopf algebra Hopf Galois theory Galois correspondence


Crespo, Teresa; Rio, Anna; Vela, Montserrat. On the Galois Correspondence Theorem in Separable Hopf Galois Theory. Publ. Mat. 60 (2016), no. 1, 221--234.

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