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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