2017, Graduate studies in mathematics, ISBN 9781470437701, Volume 183, xxi, 637 pages

Algebraic geometry -- (Co)homology theory -- Étale and other Grothendieck topologies and (co)homologies | Commutative algebra -- Instructional exposition (textbooks, tutorial papers, etc.) | Commutative algebra -- General commutative ring theory -- Ideals; multiplicative ideal theory | Separable algebras | Algebraic geometry -- Local theory -- Local structure of morphisms: Étale, flat, etc | Commutative algebra -- Ring extensions and related topics -- Galois theory | Associative rings and algebras -- Algebras and orders -- Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) | Commutative algebra -- Ring extensions and related topics -- Étale and flat extensions; Henselization; Artin approximation | Associative rings | Associative rings and algebras -- Instructional exposition (textbooks, tutorial papers, etc.) | Commutative algebra -- Theory of modules and ideals -- Class groups

Book

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

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

Parameterized differential Galois theory | Tannakian category | Differential algebra | Atiyah extension | MATHEMATICS | FIELDS | DIFFERENTIAL GALOIS THEORY | ALGEBRA | EQUATIONS | JET | DEFORMATION

Journal Article

1976, 2d ed., ISBN 9780828412841, ix, 166

Book

1983, Cotemporary mathematics, ISBN 9780821850220, Volume 24., viii, 86

Book

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

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

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

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

Polya group | Compositum of Galois extensions | Strongly ambiguous classes | Polya field | MATHEMATICS | NUMBER | TOTAL POLYNOMIALS | ALGEBRAIC-SETS

Journal Article

1989, ISBN 9780821824573, Volume no. 394., vii, 63

Book

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

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

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

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

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

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

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

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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