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Journal of Algebra, ISSN 0021-8693, 01/2018, Volume 493, pp. 1 - 19
We investigate Hopf–Galois structures on a cyclic field extension of squarefree degree . By a result of Greither and Pareigis, each such Hopf–Galois structure... 
Groups of squarefree order | Hopf–Galois structures | Field extensions | MATHEMATICS | ORDER | Hopf-Galois structures
Journal Article
Journal of Algebra, ISSN 0021-8693, 06/2018, Volume 503, pp. 389 - 408
We prove three theorems concerning the Hopf–Galois module structure of fractional ideals in a finite tamely ramified extension of -adic fields or number fields... 
Associated order | Galois module structure | Hopf–Galois structure | Hopf–Galois module theory | MATHEMATICS | Hopf-Galois module theory | Hopf-Galois structure
Journal Article
Journal of Noncommutative Geometry, ISSN 1661-6952, 2018, Volume 12, Issue 1, pp. 107 - 155
In this article we revisit the theory of homotopic Hopf-Galois extensions introduced in [9], in light of the homotopical Morita theory of comodules established... 
Hopf-Galois extension | Morita theory | Model category | Descent | MATHEMATICS | descent | MATHEMATICS, APPLIED | ALGEBRAS | MODULES | SPACES | PHYSICS, MATHEMATICAL | INDUCED MODEL STRUCTURES | CATEGORIES | model category
Journal Article
by Zhou, XY and Yang, T
COLLOQUIUM MATHEMATICUM, ISSN 0010-1354, 2019, Volume 157, Issue 2, pp. 203 - 212
Let H be a semisimple Hopf algebra over a field k and A/B be a right H-Galois extension. We establish a relationship between several Gorenstein homological... 
MATHEMATICS | Hopf-Galois extension | ALGEBRAS | PROJECTIVE-MODULES | TATE COHOMOLOGY | COHEN-MACAULAY MODULES | coherent functor | Gorenstein projective module | CROSSED-PRODUCTS | finitistic Gorenstein projective dimension | CATEGORIES | global Gorenstein projective dimension
Journal Article
Communications in Algebra, ISSN 0092-7872, 01/2017, Volume 45, Issue 1, pp. 162 - 182
Let H be a commutative weak Hopf algebra over a fixed field k, and A,B be weak H-Hopf Galois extensions. In this paper, we give a structure theorem for the... 
Morita equivalence | weak relative Hopf bimodule | 16W30 | weak Hopf-Galois extension | weak Hopf algebra | weak Hopf–Galois extension | MATHEMATICS | ALGEBRAS | MODULES | THEOREMS | II1 FACTORS | QUANTUM GROUPOIDS | Equivalence | Algebra | Theorems | Categories | Images
Journal Article
Communications in Algebra, ISSN 0092-7872, 06/2018, Volume 46, Issue 6, pp. 2534 - 2550
For p>2 prime and a a rational which is not a p n -th power for any n, the extension ℚ(w n )∕ℚ where is separable but non-normal. The Hopf-Galois theory for... 
Hopf-Galois extension | 16W30 | Greither-Pareigis theory | 12F10 | profinite extension | MATHEMATICS | Algebra
Journal Article
by Wang, Z
Acta Mathematica Hungarica, ISSN 0236-5294, 2/2018, Volume 154, Issue 1, pp. 223 - 230
We generalize [4, Theorem 4.3] to the case of Hopf–Galois extension, by introducing the cotensor product of a comodule algebra and its opposite algebra, and... 
Hopf–Galois extension | Mathematics, general | Hochschild cohomology | Mathematics | 16W30 | cotensor product | MATHEMATICS | Hopf-Galois extension | ALGEBRAS | Algebra
Journal Article
Communications in Algebra, ISSN 0092-7872, 03/2016, Volume 44, Issue 3, pp. 1119 - 1130
Let L/K be a finite Galois extension of local or global fields in any characteristic with nonabelian Galois group G, and let be an ambiguous ideal of L. We... 
Associated order | Hopf-Galois module theory | Nonabelian extension | Primary: 11R33 | Galois module structure | Hopf-Galois structure | Secondary: 11S23 | MATHEMATICS | TAME EXTENSIONS
Journal Article
Turkish Journal of Mathematics, ISSN 1300-0098, 2016, Volume 40, Issue 1, pp. 108 - 113
Journal Article
New York Journal of Mathematics, ISSN 1076-9803, 08/2018, Volume 24, pp. 451 - 457
By using a recent theorem by Koch, Kohl, Truman and Underwood on normality, we determine that some types of Hopf Galois structures do not occur on Galois... 
Hopf Galois theory | Galois correspondence | Hopf algebra | MATHEMATICS | SEPARABLE FIELD-EXTENSIONS
Journal Article
Colloquium Mathematicum, ISSN 0010-1354, 2016, Volume 143, Issue 1, pp. 127 - 147
Hopf-Galois extensions for monoidal Hom-Hopf algebras are investigated. As the main result, Schneider's affineness theorem in the case of monoidal Hom-Hopf... 
Affineness theorem | Total integrals | Hopf–Galois extensions | Monoidal Hom-Hopf algebras | LIE-ALGEBRAS | MATHEMATICS | monoidal Hom-Hopf algebras | Hopf-Galois extensions | total integrals | DEFORMATIONS | COALGEBRAS | affineness theorem | DERIVATIONS | BIALGEBRAS
Journal Article
Journal of Algebra, ISSN 0021-8693, 08/2019, Volume 531, pp. 349 - 360
In this paper, we shall determine the exact number of Hopf-Galois structures on a Galois -extension, where denotes the symmetric group on letters. 
Hopf-Galois structures | Symmetric groups | Regular subgroups | Holomorph of a finite group
Journal Article
Communications in Algebra, ISSN 0092-7872, 04/2018, Volume 46, Issue 4, pp. 1420 - 1427
Let L∕K be a finite separable extension of local or global fields in any characteristic, let be two Hopf algebras giving Hopf-Galois structures on the... 
Associated order | Hopf-Galois module theory | Galois module structure | Primary: 11R33 | Hopf-Galois structure | Secondary: 11S23 | Hopf–Galois structure | Hopf–Galois module theory | MATHEMATICS
Journal Article
Journal of Algebra and its Applications, ISSN 0219-4988, 09/2018, Volume 17, Issue 9
Let (H, alpha) be a Frobenius monoidal Hom-Hopf algebra, and (A, beta) an (H*, alpha*(-1))-Hom-Hopf Galois extension of (A(H), beta vertical bar H-A). We prove... 
Frobenius monoidal Hom-Hopf algebra | trace one element | Hom-crossed product | Hom-Hopf Galois extension | LIE-ALGEBRAS | MATHEMATICS | MATHEMATICS, APPLIED | DEFORMATIONS | DERIVATIONS
Journal Article
Journal of Algebra, ISSN 0021-8693, 05/2013, Volume 381, pp. 131 - 139
Let be a finite Galois extension of fields with group . When is nilpotent, we show that the problem of enumerating all nilpotent Hopf–Galois structures on can... 
Field extension | Hopf–Galois structure | Abelian group | Nilpotent group | Hopf-Galois structure | MATHEMATICS
Journal Article
NEW YORK JOURNAL OF MATHEMATICS, ISSN 1076-9803, 2019, Volume 25, pp. 219 - 237
Let L/F be a Galois extension of fields with Galois group isomorphic to the quaternion group of order 8. We describe all of the Hopf-Galois structures admitted... 
MATHEMATICS | Wedderburn-Artin decomposition | Hopf Galois structure | Hopf algebra | Galois extension
Journal Article
Acta Mathematica Hungarica, ISSN 0236-5294, 1/2013, Volume 138, Issue 1, pp. 140 - 146
Let H be a weak Hopf algebra, A a right weak H-comodule algebra and B the subalgebra of the H-coinvariant elements of A. Let A/B be a right weak H-Galois... 
weak Hopf module | global dimension | 16W30 | 16E10 | weak Hopf–Galois extension | Maschke-type theorem | Mathematics, general | Mathematics | weak Hopf-Galois extension | MATHEMATICS | ALGEBRAS | THEOREM | Algebra
Journal Article
Journal de Theorie des Nombres de Bordeaux, ISSN 1246-7405, 2016, Volume 28, Issue 2, pp. 557 - 582
Journal Article
Filomat, ISSN 0354-5180, 1/2016, Volume 30, Issue 10, pp. 2825 - 2828
Let 𝐻 be a finite dimensional weak Hopf algebra and 𝐴/𝐵 be a right faithfully flat weak 𝐻-Galois extension. Then in this note, we first show that if 𝐻 is... 
Algebra | Mathematical theorems | Adjoints | Subalgebras | Functors | Mathematics | Mathematical duality | Galois theory | Weak hopf-galois extension | Finitistic dimension | Duality theorem | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | THEOREM | Weak Hopf-Galois extension | DUALITY
Journal Article
Communications in Algebra, ISSN 0092-7872, 09/2017, Volume 45, Issue 9, pp. 3892 - 3892
We regret that we must issue a correction to the above article, which slightly reduces the scope of the main theorem. 
Associated order | Hopf-Galois module theory | Primary: 11R33 | Galois module structure | nonabelian extension | Hopf-Galois structure | Secondary: 11S23 | MATHEMATICS | Theorems | Modules | Algebra
Journal Article
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