Algebraic Division Ring Extensions

Algebraic Division Ring Extensions1

Realizability of Algebraic Galois Extensions by Strictly Commutative Ring Spectra

We discuss some of the basic ideas of Galois theory for commutative S-algebras originally formulated by John Rognes. We restrict attention to the case of finite Galois groups and to global Galois extensions. We describe parts of the general framework developed by Rognes. Central rôles are played by the notion of strong duality and a trace mapping constructed by Greenlees and May in the context ...

Realisibility of Algebraic Galois Extensions by Strictly Commutative Ring Spectra

We describe some of the basic ideas of Galois theory for commutative S-algebras originally formulated by John Rognes. We restrict attention to the case of finite Galois groups. We describe the general framework developed by Rognes. Central rôles are played by the notion of strong duality and a trace or norm mapping constructed by Greenlees and May in the context of generalized Tate cohomology. ...

Algebraic Extensions of Normed Algebras

Disclaimer: This dissertation does not contain plagiarised material; except where otherwise stated all theorems are the author's. Acknowledgement: Many thanks to Joel Feinstein for guidance with the literature, useful suggestions and comments on this work.

Algebraic Extensions for Symbolic Summation

The main result of this thesis is an effective method to extend Karr’s symbolic summation framework to algebraic extensions. These arise, for example, when working with expressions involving (−1)n. An implementation of this method, including a modernised version of Karr’s algorithm is also presented. Karr’s algorithm is the summation analogue of the Risch algorithm for indefinite integration. I...