Cyclic Galois extensions of commutative rings Cornelius Greither.

By:

Greither, Cornelius

Material type: Text

TextLanguage: English Series: Lecture notes in mathematics (Springer-Verlag) ; 1534.Publication details: Berlin ; New York : Springer-Verlag, c1992.Description: 1 online resource (x, 145 p.) : illISBN:

9783540475392 (electronic bk.)
3540475397 (electronic bk.)

Subject(s):

Contents:

Galois theory of commutative rings Cornelius Greither Pages 1-31 PDF Cyclotomic descent Cornelius Greither Pages 32-54 Corestriction and Hilbert's Theorem 90 Cornelius Greither Pages 55-66 Calculations with units Cornelius Greither Pages 67-76 Cyclic p-extensions and {ie771-}-extensions of number fields Cornelius Greither Pages 77-96 Geometric theory: cyclic extensions of finitely generated fields Cornelius Greither Pages 97-108 Cyclic Galois theory without the condition “p −1 ≥ R” Cornelius Greither Pages 109-139 Back Matter Pages 140-145

Summary: The structure theory of abelian extensions of commutative rings is a subjectwhere commutative algebra and algebraic number theory overlap. This exposition is aimed at readers with some background in either of these two fields. Emphasis is given to the notion of a normal basis, which allows one to view in a well-known conjecture in number theory (Leopoldt's conjecture) from a new angle. Methods to construct certain extensions quite explicitly are also described at length.

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Includes bibliographical references (p. [140]-143) and index.

Galois theory of commutative rings
Cornelius Greither
Pages 1-31
PDF
Cyclotomic descent Cornelius Greither Pages 32-54
Corestriction and Hilbert's Theorem 90 Cornelius Greither Pages 55-66
Calculations with units Cornelius Greither Pages 67-76
Cyclic p-extensions and {ie771-}-extensions of number fields Cornelius Greither Pages 77-96
Geometric theory: cyclic extensions of finitely generated fields Cornelius Greither Pages 97-108
Cyclic Galois theory without the condition “p −1 ≥ R”
Cornelius Greither Pages 109-139
Back Matter Pages 140-145

Online version restricted to NUS staff and students only through NUSNET.

The structure theory of abelian extensions of commutative rings is a subjectwhere commutative algebra and algebraic number theory overlap. This exposition is aimed at readers with some background in either of these two fields. Emphasis is given to the notion of a normal basis, which allows one to view in a well-known conjecture in number theory (Leopoldt's conjecture) from a new angle. Methods to construct certain extensions quite explicitly are also described at length.

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