Cyclic Galois Extensions of Commutative Rings
Greither, Cornelius.
Cyclic Galois Extensions of Commutative Rings [electronic resource] / by Cornelius Greither. - X, 146 p. online resource. - Lecture Notes in Mathematics, 1534 0075-8434 ; . - Lecture Notes in Mathematics, 1534 .
Galois theory of commutative rings -- Cyclotomic descent -- Corestriction and Hilbert's Theorem 90 -- Calculations with units -- Cyclic p-extensions and -extensions of number fields -- Geometric theory: cyclic extensions of finitely generated fields -- Cyclic Galois theory without the condition “p ?1 ? R”.
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.
9783540475392
10.1007/BFb0089165 doi
Number theory.
Algebra.
Number Theory.
Algebra.
QA241-247.5
512.7
Cyclic Galois Extensions of Commutative Rings [electronic resource] / by Cornelius Greither. - X, 146 p. online resource. - Lecture Notes in Mathematics, 1534 0075-8434 ; . - Lecture Notes in Mathematics, 1534 .
Galois theory of commutative rings -- Cyclotomic descent -- Corestriction and Hilbert's Theorem 90 -- Calculations with units -- Cyclic p-extensions and -extensions of number fields -- Geometric theory: cyclic extensions of finitely generated fields -- Cyclic Galois theory without the condition “p ?1 ? R”.
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.
9783540475392
10.1007/BFb0089165 doi
Number theory.
Algebra.
Number Theory.
Algebra.
QA241-247.5
512.7