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1984, Encyclopedia of mathematics and its applications, ISBN 9780201135213, Volume 22, li, 294
Originally published in 1984, the principal objective of this book is to make the general theory of field extensions accessible to any reader with a modest... 
Field extensions (Mathematics) | Galois theory
Book
2000, Mathematical surveys and monographs, ISBN 9780821821312, Volume 80, viii, 215
Book
Advances in Mathematics, ISSN 0001-8708, 05/2013, Volume 238, pp. 322 - 411
Generalizing Atiyah extensions, we introduce and study differential abelian tensor categories over differential rings. By a differential ring, we mean a... 
Parameterized differential Galois theory | Tannakian category | Differential algebra | Atiyah extension | MATHEMATICS | FIELDS | DIFFERENTIAL GALOIS THEORY | ALGEBRA | EQUATIONS | JET | DEFORMATION
Journal Article
1992, Lecture notes in mathematics, ISBN 0387563504, Volume 1534., x, 145
The structure theory of abelian extensions of commutative rings is a subjectwhere commutative algebra and algebraic number theory overlap. This exposition is... 
Commutative rings | Ring extensions (Algebra) | Galois theory | Number theory | Algebra
Book
1989, Contemporary mathematics, ISBN 9780821851012, Volume 95., xv, 104
Book
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
Topology and its Applications, ISSN 0166-8641, 02/2018, Volume 235, pp. 290 - 338
We establish a formal framework for Rognes's homotopical Galois theory and adapt it to the context of motivic spaces and spectra. We discuss examples of Galois... 
Model category | Motivic homotopy theory | Galois theory | MATHEMATICS | MATHEMATICS, APPLIED | COHOMOLOGY | OPERATIONS | SPACES | MODEL CATEGORIES | HERMITIAN K-THEORY
Journal Article
Journal of Number Theory, ISSN 0022-314X, 10/2019, Volume 203, pp. 360 - 375
The Pólya group of a number field is the subgroup of the class group of generated by the classes of the products of the maximal ideals with same norm. A Pólya... 
Polya group | Compositum of Galois extensions | Strongly ambiguous classes | Polya field | MATHEMATICS | NUMBER | TOTAL POLYNOMIALS | ALGEBRAIC-SETS
Journal Article
Journal of Algebra, ISSN 0021-8693, 01/2015, Volume 422, pp. 187 - 222
Given a field and a finite group , is a finite Galois extension of of Galois group containing which is regular over and has all the Galois extensions of of... 
Field arithmetic | Galois theory | MATHEMATICS | COVERS | FUNCTION-FIELDS | MODULI SPACES
Journal Article
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
Advances in Mathematics, ISSN 0001-8708, 01/2016, Volume 287, pp. 31 - 108
We establish a Galois-theoretic interpretation of cohomology in semi-abelian categories: cohomology with trivial coefficients classifies central extensions,... 
Higher central extension | Semi-abelian category | Cohomology | Categorical Galois theory | Torsor | GALOIS THEORY | HOPF FORMULAS | 3X3 LEMMA | MATHEMATICS | COMMUTATOR THEORY | MALCEV CATEGORIES | GROUPOIDS | SEMI-ABELIAN CATEGORIES | HOMOLOGY | DIRECTIONS | Mathematics - Category Theory
Journal Article
1984, ISBN 0821823124, Volume no. 309., vii, 71
Book
Journal of Algebra, ISSN 0021-8693, 02/2017, Volume 471, pp. 193 - 219
Given an arbitrary field , we describe all Galois extensions whose Galois groups are isomorphic to the group of upper triangular unipotent 4-by-4 matrices with... 
Local fields | Norm maps | Galois unipotent extensions | Trace maps | Dihedral group | MATHEMATICS | MASSEY PRODUCTS | P-EXTENSIONS | FIELD
Journal Article
06/2008, Lecture Notes in Mathematics Ser., ISBN 3540563504
Annotation The structure theory of abelian extensions of commutativerings is a subjectwhere commutative algebra and algebraicnumber theory overlap. This... 
Rings (Algebra) | Galois Theory | Mathematics | Commutative Rings
Web Resource
06/2008, Lecture Notes in Mathematics Ser., ISBN 3540563504
Annotation The structure theory of abelian extensions of commutativerings is a subjectwhere commutative algebra and algebraicnumber theory overlap. This... 
Rings (Algebra) | Galois Theory | Mathematics | Commutative Rings
Web Resource
Linear Algebra and Its Applications, ISSN 0024-3795, 05/2019, Volume 568, pp. 39 - 83
In this paper, we develop an arithmetic theory of quadratic and hermitian forms over infinite algebraic extensions of local and global fields. In particular,... 
Orthogonal groups | Quadratic forms | Hermitian forms | Hasse principles | Algebraic groups | Unitary groups | Global fields | MATHEMATICS | MATHEMATICS, APPLIED | GALOIS COHOMOLOGY | SEMISIMPLE GROUPS | Theorems | Algebra | Fields (mathematics) | Group theory | Linear algebra
Journal Article
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