Ebook: Cyclic Galois Extensions of Commutative Rings

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

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