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
AbstractLet R be a commutative ring with identity, and let S be an R-algebra. Let M denote the maxim...
It is well known that the Galois group of an extension L/F puts con-straints on the structure of the...
Let L=K be an extension of algebraic number fields, where L is abelian over Q . In this paper we gi...
AbstractLet K be a cyclic Galois extension of Q of finite degree. We give two algorithms to construc...
Let L/K be an extension of number fields where L/ℚ is abelian. We define such an extension to be Leo...
In this thesis we consider three main problems: the Galois module structure of rings of integers in ...
Abstract: If L/K is a finite Galois extension of local fields, we say that the val-uation criterion ...
In this thesis we define the notion of a Galois extension of commutative rings, and present the anal...
In this thesis we define the notion of a Galois extension of commutative rings, and present the anal...
We develop a method to compute a basis of the associated order in a Hopf Galois structure H of the r...
We develop a method to compute a basis of the associated order in a Hopf Galois structure H of the r...
We develop a method to compute a basis of the associated order in a Hopf Galois structure H of the r...
The focus of this thesis is to use Galois Theory to prove results in Number Theory. As a result, we ...
Let L/K be a finite, Galois extension of local or global fields. In the classical setting of additiv...
Let L/K be a finite, Galois extension of local or global fields. In the classical setting of additiv...
AbstractLet R be a commutative ring with identity, and let S be an R-algebra. Let M denote the maxim...
It is well known that the Galois group of an extension L/F puts con-straints on the structure of the...
Let L=K be an extension of algebraic number fields, where L is abelian over Q . In this paper we gi...
AbstractLet K be a cyclic Galois extension of Q of finite degree. We give two algorithms to construc...
Let L/K be an extension of number fields where L/ℚ is abelian. We define such an extension to be Leo...
In this thesis we consider three main problems: the Galois module structure of rings of integers in ...
Abstract: If L/K is a finite Galois extension of local fields, we say that the val-uation criterion ...
In this thesis we define the notion of a Galois extension of commutative rings, and present the anal...
In this thesis we define the notion of a Galois extension of commutative rings, and present the anal...
We develop a method to compute a basis of the associated order in a Hopf Galois structure H of the r...
We develop a method to compute a basis of the associated order in a Hopf Galois structure H of the r...
We develop a method to compute a basis of the associated order in a Hopf Galois structure H of the r...
The focus of this thesis is to use Galois Theory to prove results in Number Theory. As a result, we ...
Let L/K be a finite, Galois extension of local or global fields. In the classical setting of additiv...
Let L/K be a finite, Galois extension of local or global fields. In the classical setting of additiv...
AbstractLet R be a commutative ring with identity, and let S be an R-algebra. Let M denote the maxim...
It is well known that the Galois group of an extension L/F puts con-straints on the structure of the...
Let L=K be an extension of algebraic number fields, where L is abelian over Q . In this paper we gi...
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