Cyclic Galois extensions of commutative rings
Greither, Cornelius.
Cyclic Galois extensions of commutative rings Cornelius Greither. - Berlin ; New York : Springer-Verlag, c1992. - 1 online resource (x, 145 p.) : ill. - Lecture notes in mathematics, 1534. 0075-8434 ; . - Lecture notes in mathematics (Springer-Verlag) ; 1534. .
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 -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.
Mode of access: World Wide Web.
System requirements: Internet connectivity; World Wide Web browser.
9783540475392 (electronic bk.) 3540475397 (electronic bk.)
Commutative rings.
Galois theory.
Ring extensions (Algebra), Galois theory algebra algebraic number theory commutative algebra commutative ring number theory
Cyclic Galois extensions of commutative rings Cornelius Greither. - Berlin ; New York : Springer-Verlag, c1992. - 1 online resource (x, 145 p.) : ill. - Lecture notes in mathematics, 1534. 0075-8434 ; . - Lecture notes in mathematics (Springer-Verlag) ; 1534. .
Includes bibliographical references (p. [140]-143) and index.
Galois theory of commutative rings
Cornelius Greither
Pages 1-31
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 -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.
Mode of access: World Wide Web.
System requirements: Internet connectivity; World Wide Web browser.
9783540475392 (electronic bk.) 3540475397 (electronic bk.)
Commutative rings.
Galois theory.
Ring extensions (Algebra), Galois theory algebra algebraic number theory commutative algebra commutative ring number theory