Title: Cyclic Galois extensions of commutative rings
Description: 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.
Subjects: Commutative rings, Galois theory, Ring extensions (Algebra), Rings (algebra), Mathematics, Algebra, Number theory